OEIS Similars: A122848, A104556, A096713
↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
---|---|---|---|
Std | TriangleT(n, k), 0 ≤ k ≤ n | A122848 | 1 0 1 0 1 1 0 0 3 1 0 0 3 6 1 0 0 0 15 10 1 0 0 0 15 45 15 1 0 0 0 0 105 105 21 1 0 0 0 0 105 420 |
Std | RevT(n, n - k), 0 ≤ k ≤ n | A144299 | 1 1 0 1 1 0 1 3 0 0 1 6 3 0 0 1 10 15 0 0 0 1 15 45 15 0 0 0 1 21 105 105 0 0 0 0 1 28 210 420 105 |
Std | InvT-1(n, k), 0 ≤ k ≤ n | A132062 | 1 0 1 0 -1 1 0 3 -3 1 0 -15 15 -6 1 0 105 -105 45 -10 1 0 -945 945 -420 105 -15 1 0 10395 -10395 |
Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 -1 0 1 -3 3 0 1 -6 15 -15 0 1 -10 45 -105 105 0 1 -15 105 -420 945 -945 0 1 -21 210 -1260 |
Std | Accsee docs | missing | 1 0 1 0 1 2 0 0 3 4 0 0 3 9 10 0 0 0 15 25 26 0 0 0 15 60 75 76 0 0 0 0 105 210 231 232 0 0 0 0 105 |
Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 4 4 4 1 7 10 10 10 1 11 26 26 26 26 1 16 61 76 76 76 76 1 22 127 232 232 232 232 232 |
Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 0 1 0 0 3 0 0 3 1 0 0 0 6 0 0 0 15 1 0 0 0 15 10 0 0 0 0 45 1 0 0 0 0 105 15 0 0 0 0 |
Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 0 9 4 0 0 9 24 5 0 0 0 60 50 6 0 0 0 60 225 90 7 0 0 0 0 525 630 147 8 0 0 0 0 525 |
Std | RowSum∑ k=0..n T(n, k) | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Std | EvenSum∑ k=0..n T(n, k) even(k) | A085386 | 1 0 1 3 4 10 46 126 316 1296 5356 17380 63856 296088 1264264 4940040 22302736 110455936 507711376 |
Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 1 1 6 16 30 106 448 1324 4140 18316 76296 272416 1126216 5409496 23904000 101343376 489602448 |
Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001464 | 1 -1 0 2 -2 -6 16 20 -132 -28 1216 -936 -12440 23672 138048 -469456 -1601264 9112560 18108928 |
Std | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 1 1 3 4 6 16 25 46 120 211 441 1156 2233 5104 13581 28351 69345 188101 419320 1082566 2998776 |
Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 7 22 66 226 778 2892 10972 43876 179796 766888 3352792 15144312 70042456 333064336 1619336208 |
Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001475 | 1 2 5 13 38 116 382 1310 4748 17848 70076 284252 1195240 5174768 23103368 105899656 498656912 |
Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
Std | ColMiddleT(n, n // 2) | A123023 | 1 0 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 0 |
Std | CentralET(2 n, n) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
Std | ColLeftT(n, 0) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 3 10 43 201 1066 6028 36975 238843 1637191 11718246 87877648 683880640 5530539288 46195085056 |
Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -1 -8 -5 101 286 -1616 -10513 26515 404011 -174844 -17016416 -26519648 782613560 2994914896 |
Std | TransNat0∑ k=0..n T(n, k) k | A189940 | 0 1 3 9 28 90 306 1078 3984 15228 60580 248556 1055088 4606264 20712888 95550120 452450176 |
Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A001475 | 1 2 5 13 38 116 382 1310 4748 17848 70076 284252 1195240 5174768 23103368 105899656 498656912 |
Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 21 82 320 1266 5110 21176 89892 392140 1752476 8036040 37709776 181213592 889901160 |
Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A047974 | 1 1 3 7 25 81 331 1303 5937 26785 133651 669351 3609673 19674097 113525595 664400311 4070168161 |
Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A293604 | 1 1 -1 -5 1 41 31 -461 -895 6481 22591 -107029 -604031 1964665 17669471 -37341149 -567425279 |
Std | DiagRow1T(n + 1, n) | A000217 | 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 |
Std | DiagRow2T(n + 2, n) | A050534 | 0 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
Std | DiagRow3T(n + 3, n) | A240440 | 0 0 0 15 105 420 1260 3150 6930 13860 25740 45045 75075 120120 185640 278460 406980 581400 813960 |
Std | DiagCol1T(n + 1, 1) | A019590 | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Std | DiagCol2T(n + 2, 2) | missing | 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Std | DiagCol3T(n + 3, 3) | missing | 1 6 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 4 6 3 1 0 10 20 12 4 1 0 26 76 54 20 5 1 0 76 312 270 112 30 6 1 0 232 1384 |
Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 |
Std | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
Std | PolyRow3∑ k=0..3 T(3, k) n^k | A366151 | 0 4 20 54 112 200 324 490 704 972 1300 1694 2160 2704 3332 4050 4864 5780 6804 7942 9200 10584 |
Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000898 | 1 2 6 20 76 312 1384 6512 32400 168992 921184 5222208 30710464 186753920 1171979904 7573069568 |
Std | PolyCol3∑ k=0..n T(n, k) 3^k | A335819 | 1 3 12 54 270 1458 8424 51516 331452 2230740 15641424 113846472 857706408 6671592216 53465326560 |
Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 6 54 688 11250 224856 5311012 144740352 4470481692 154319500000 5887775897256 246030662283264 |
Alt | TriangleT(n, k), 0 ≤ k ≤ n | A122848 | 1 0 -1 0 -1 1 0 0 3 -1 0 0 3 -6 1 0 0 0 -15 10 -1 0 0 0 -15 45 -15 1 0 0 0 0 105 -105 21 -1 0 0 0 0 |
Alt | RevT(n, n - k), 0 ≤ k ≤ n | A144299 | 1 -1 0 1 -1 0 -1 3 0 0 1 -6 3 0 0 -1 10 -15 0 0 0 1 -15 45 -15 0 0 0 -1 21 -105 105 0 0 0 0 1 -28 |
Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 -3 -3 1 0 -21 -21 6 1 0 165 165 -45 -10 1 0 3375 3375 -930 -195 15 1 0 -51345 -51345 |
Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -3 -3 0 1 6 -21 -21 0 1 -10 -45 165 165 0 1 15 -195 -930 3375 3375 0 1 -21 -210 2940 |
Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 0 3 2 0 0 3 -3 -2 0 0 0 -15 -5 -6 0 0 0 -15 30 15 16 0 0 0 0 105 0 21 20 0 0 0 0 |
Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 2 2 2 1 -5 -2 -2 -2 -1 9 -6 -6 -6 -6 1 -14 31 16 16 16 16 -1 20 -85 20 20 20 20 20 |
Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -1 0 0 1 0 0 3 0 0 3 -1 0 0 0 -6 0 0 0 -15 1 0 0 0 -15 10 0 0 0 0 45 -1 0 0 0 0 105 -15 |
Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 0 9 -4 0 0 9 -24 5 0 0 0 -60 50 -6 0 0 0 -60 225 -90 7 0 0 0 0 525 -630 147 -8 0 0 |
Alt | RowSum∑ k=0..n T(n, k) | A001464 | 1 -1 0 2 -2 -6 16 20 -132 -28 1216 -936 -12440 23672 138048 -469456 -1601264 9112560 18108928 |
Alt | EvenSum∑ k=0..n T(n, k) even(k) | A085386 | 1 0 1 3 4 10 46 126 316 1296 5356 17380 63856 296088 1264264 4940040 22302736 110455936 507711376 |
Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -1 -1 -6 -16 -30 -106 -448 -1324 -4140 -18316 -76296 -272416 -1126216 -5409496 -23904000 |
Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Alt | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -1 1 3 2 -6 -14 -5 44 90 1 -399 -736 287 4348 7281 -6301 -55485 -84149 121330 812294 1106754 |
Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 5 -2 -26 46 146 -580 -748 7156 604 -92696 96680 1270088 -2955016 -18167024 72958576 |
Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 1 5 -10 -16 82 34 -740 440 7436 -12772 -81464 258400 938680 -5025736 -10655728 100180064 |
Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
Alt | ColMiddleT(n, n // 2) | A123023 | 1 0 -1 0 3 0 -15 0 105 0 -945 0 10395 0 -135135 0 2027025 0 -34459425 0 654729075 0 -13749310575 0 |
Alt | CentralET(2 n, n) | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
Alt | ColLeftT(n, 0) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 -1 8 -5 -101 286 1616 -10513 -26515 404011 174844 -17016416 26519648 782613560 -2994914896 |
Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -10 43 -201 1066 -6028 36975 -238843 1637191 -11718246 87877648 -683880640 5530539288 |
Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 1 3 -8 -10 66 14 -608 468 6220 -11836 -69024 234728 800632 -4556280 -9054464 91067504 80967312 |
Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 1 5 -10 -16 82 34 -740 440 7436 -12772 -81464 258400 938680 -5025736 -10655728 100180064 |
Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 3 -26 0 246 -238 -2568 5436 28900 -105996 -337512 2055248 3795624 -41212200 -32229824 |
Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A293604 | 1 -1 -1 5 1 -41 31 461 -895 -6481 22591 107029 -604031 -1964665 17669471 37341149 -567425279 |
Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A047974 | 1 -1 3 -7 25 -81 331 -1303 5937 -26785 133651 -669351 3609673 -19674097 113525595 -664400311 |
Alt | DiagRow1T(n + 1, n) | A000217 | 0 -1 3 -6 10 -15 21 -28 36 -45 55 -66 78 -91 105 -120 136 -153 171 -190 210 -231 253 -276 300 -325 |
Alt | DiagRow2T(n + 2, n) | A050534 | 0 0 3 -15 45 -105 210 -378 630 -990 1485 -2145 3003 -4095 5460 -7140 9180 -11628 14535 -17955 21945 |
Alt | DiagRow3T(n + 3, n) | A240440 | 0 0 0 -15 105 -420 1260 -3150 6930 -13860 25740 -45045 75075 -120120 185640 -278460 406980 -581400 |
Alt | DiagCol1T(n + 1, 1) | A019590 | -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Alt | DiagCol2T(n + 2, 2) | missing | 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Alt | DiagCol3T(n + 3, 3) | missing | -1 -6 -15 -15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 2 2 -3 1 0 -2 4 6 -4 1 0 -6 -20 0 12 -5 1 0 16 8 -54 -16 20 -6 1 0 20 184 |
Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 2 4 0 -16 -50 -108 -196 -320 -486 -700 -968 -1296 -1690 -2156 -2700 -3328 -4046 -4860 -5776 -6800 |
Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A062267 | 1 -2 2 4 -20 8 184 -464 -1648 10720 8224 -230848 280768 4978816 -17257600 -104891648 727511296 |
Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 6 0 -54 162 324 -3888 4860 78732 -367416 -1259712 15903864 -2361960 -613164816 1938696768 |
Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 2 0 -80 1250 -14904 134456 -225280 -31886460 1130500000 -26814347296 454786265088 |
Rev | TriangleT(n, k), 0 ≤ k ≤ n | A144299 | 1 1 0 1 1 0 1 3 0 0 1 6 3 0 0 1 10 15 0 0 0 1 15 45 15 0 0 0 1 21 105 105 0 0 0 0 1 28 210 420 105 |
Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A132062 | 1 0 1 0 -1 1 0 3 -3 1 0 -15 15 -6 1 0 105 -105 45 -10 1 0 -945 945 -420 105 -15 1 0 10395 -10395 |
Rev | Accsee docs | missing | 1 1 1 1 2 2 1 4 4 4 1 7 10 10 10 1 11 26 26 26 26 1 16 61 76 76 76 76 1 22 127 232 232 232 232 232 |
Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 0 3 4 0 0 3 9 10 0 0 0 15 25 26 0 0 0 15 60 75 76 0 0 0 0 105 210 231 232 0 0 0 0 105 |
Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 3 0 1 6 0 1 10 3 0 1 15 15 0 1 21 45 0 0 1 28 105 15 0 1 36 210 105 0 0 1 45 378 420 |
Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 6 0 0 1 12 9 0 0 1 20 45 0 0 0 1 30 135 60 0 0 0 1 42 315 420 0 0 0 0 1 56 630 1680 |
Rev | RowSum∑ k=0..n T(n, k) | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Rev | EvenSum∑ k=0..n T(n, k) even(k) | A000704 | 1 1 1 1 4 16 46 106 316 1324 5356 18316 63856 272416 1264264 5409496 22302736 101343376 507711376 |
Rev | OddSum∑ k=0..n T(n, k) odd(k) | A001465 | 0 0 1 3 6 10 30 126 448 1296 4140 17380 76296 296088 1126216 4940040 23904000 110455936 489602448 |
Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
Rev | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 2 4 7 14 31 67 149 352 844 2051 5152 13219 34367 91219 246766 676652 1884169 5330122 15275249 |
Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001475 | 1 2 5 13 38 116 382 1310 4748 17848 70076 284252 1195240 5174768 23103368 105899656 498656912 |
Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 3 7 22 66 226 778 2892 10972 43876 179796 766888 3352792 15144312 70042456 333064336 1619336208 |
Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
Rev | ColMiddleT(n, n // 2) | A133221 | 1 1 1 3 3 15 15 105 105 945 945 10395 10395 135135 135135 2027025 2027025 34459425 34459425 |
Rev | CentralET(2 n, n) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
Rev | CentralOT(2 n + 1, n) | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Rev | ColRightT(n, n) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 3 10 43 201 1066 6028 36975 238843 1637191 11718246 87877648 683880640 5530539288 46195085056 |
Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -1 8 -5 -101 286 1616 -10513 -26515 404011 174844 -17016416 26519648 782613560 -2994914896 |
Rev | TransNat0∑ k=0..n T(n, k) k | A162970 | 0 0 1 3 12 40 150 546 2128 8352 34380 144100 626736 2784288 12753832 59692920 286857600 1407536896 |
Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 3 7 22 66 226 778 2892 10972 43876 179796 766888 3352792 15144312 70042456 333064336 1619336208 |
Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A174764 | 0 0 1 3 18 70 330 1386 6328 28008 130140 603460 2895816 14024088 69786808 352043160 1817317440 |
Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000898 | 1 2 6 20 76 312 1384 6512 32400 168992 921184 5222208 30710464 186753920 1171979904 7573069568 |
Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A062267 | 1 -2 2 4 -20 8 184 -464 -1648 10720 8224 -230848 280768 4978816 -17257600 -104891648 727511296 |
Rev | DiagRow1T(n + 1, n) | A019590 | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Rev | DiagRow2T(n + 2, n) | missing | 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Rev | DiagRow3T(n + 3, n) | missing | 1 6 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Rev | DiagCol1T(n + 1, 1) | A000217 | 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 |
Rev | DiagCol2T(n + 2, 2) | A050534 | 0 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
Rev | DiagCol3T(n + 3, 3) | A240440 | 0 0 0 15 105 420 1260 3150 6930 13860 25740 45045 75075 120120 185640 278460 406980 581400 813960 |
Rev | Polysee docs | A359762 | 1 1 1 1 1 1 1 2 1 1 1 4 3 1 1 1 10 7 4 1 1 1 26 25 10 5 1 1 1 76 81 46 13 6 1 1 1 232 331 166 73 16 |
Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A016777 | 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 |
Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A047974 | 1 1 3 7 25 81 331 1303 5937 26785 133651 669351 3609673 19674097 113525595 664400311 4070168161 |
Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A115327 | 1 1 4 10 46 166 856 3844 21820 114076 703216 4125496 27331624 175849480 1241782816 8627460976 |
Rev | PolyDiag∑ k=0..n T(n, k) n^k | A277614 | 1 1 3 10 73 426 4951 41308 658785 7149628 144963451 1937124696 47660873833 756536698360 |
Inv | TriangleT(n, k), 0 ≤ k ≤ n | A132062 | 1 0 1 0 -1 1 0 3 -3 1 0 -15 15 -6 1 0 105 -105 45 -10 1 0 -945 945 -420 105 -15 1 0 10395 -10395 |
Inv | RevT(n, n - k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 -1 0 1 -3 3 0 1 -6 15 -15 0 1 -10 45 -105 105 0 1 -15 105 -420 945 -945 0 1 -21 210 -1260 |
Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A144299 | 1 1 0 1 1 0 1 3 0 0 1 6 3 0 0 1 10 15 0 0 0 1 15 45 15 0 0 0 1 21 105 105 0 0 0 0 1 28 210 420 105 |
Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 3 0 1 0 -15 0 -6 -5 0 105 0 45 35 36 0 -945 0 -420 -315 -330 -329 0 10395 0 4725 |
Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -2 1 1 1 -5 10 -5 -5 1 -9 36 -69 36 36 1 -14 91 -329 616 -329 -329 1 -20 190 -1070 |
Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 3 1 0 -15 -3 0 105 15 1 0 -945 -105 -6 0 10395 945 45 1 0 -135135 -10395 -420 -10 0 |
Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 6 -9 4 0 -30 45 -24 5 0 210 -315 180 -50 6 0 -1890 2835 -1680 525 -90 7 0 20790 |
Inv | RowSum∑ k=0..n T(n, k) | A278990 | 1 1 0 1 -5 36 -329 3655 -47844 721315 -12310199 234615096 -4939227215 113836841041 -2850860253240 |
Inv | EvenSum∑ k=0..n T(n, k) even(k) | A036244 | 1 0 1 -3 16 -115 1051 -11676 152839 -2304261 39325276 -749484505 15778499881 -363654981768 |
Inv | OddSum∑ k=0..n T(n, k) odd(k) | A025164 | 0 1 -1 4 -21 151 -1380 15331 -200683 3025576 -51635475 984099601 -20717727096 477491822809 |
Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A001515 | 1 -1 2 -7 37 -266 2431 -27007 353522 -5329837 90960751 -1733584106 36496226977 -841146804577 |
Inv | AbsSum∑ k=0..n | T(n, k) | | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 4 -18 121 -1056 11386 -145960 2166991 -36550095 690151981 -14420529291 330298370704 |
Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 4 -26 221 -2339 29569 -434251 7260994 -136133504 2827691351 -64444568891 1598655001789 |
Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A003436 | 1 2 1 1 -4 31 -293 3326 -44189 673471 -11588884 222304897 -4704612119 108897613826 -2737023412199 |
Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 30 630 3780 207900 8108100 56756700 1929727800 329983453800 549972423000 139143023019000 |
Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
Inv | RowMaxMax k=0..n | T(n, k) | | A001147 | 1 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
Inv | ColMiddleT(n, n // 2) | missing | 1 0 -1 3 15 -105 -420 4725 17325 -270270 -945945 18918900 64324260 -1571349780 -5237832600 |
Inv | CentralET(2 n, n) | A376872 | 1 -1 15 -420 17325 -945945 64324260 -5237832600 496939367925 -53835098191875 6557114959770375 |
Inv | CentralOT(2 n + 1, n) | missing | 0 3 -105 4725 -270270 18918900 -1571349780 151242416325 -16564645597500 2034966711652875 |
Inv | ColLeftT(n, 0) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -1 1 7 -124 1591 -19991 256691 -3335228 41759236 -430787224 595905949 182463444151 |
Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 19 175 2076 29911 505093 9757539 211883500 5102919316 134868653976 3878398876573 |
Inv | TransNat0∑ k=0..n T(n, k) k | A278990 | 0 1 1 0 1 -5 36 -329 3655 -47844 721315 -12310199 234615096 -4939227215 113836841041 -2850860253240 |
Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A003436 | 1 2 1 1 -4 31 -293 3326 -44189 673471 -11588884 222304897 -4704612119 108897613826 -2737023412199 |
Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 0 7 -45 396 -4277 54825 -813348 13704985 -258514179 5396147208 -123480680375 3073594708107 |
Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A002119 | 1 1 -1 7 -71 1001 -18089 398959 -10391023 312129649 -10622799089 403978495031 -16977719590391 |
Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001517 | 1 1 3 19 193 2721 49171 1084483 28245729 848456353 28875761731 1098127402131 46150226651233 |
Inv | DiagRow1T(n + 1, n) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
Inv | DiagRow2T(n + 2, n) | A050534 | 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
Inv | DiagRow3T(n + 3, n) | A240440 | 0 -15 -105 -420 -1260 -3150 -6930 -13860 -25740 -45045 -75075 -120120 -185640 -278460 -406980 |
Inv | DiagCol1T(n + 1, 1) | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
Inv | DiagCol2T(n + 2, 2) | A001147 | 1 -3 15 -105 945 -10395 135135 -2027025 34459425 -654729075 13749310575 -316234143225 7905853580625 |
Inv | DiagCol3T(n + 3, 3) | A001879 | 1 -6 45 -420 4725 -62370 945945 -16216200 310134825 -6547290750 151242416325 -3794809718700 |
Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 1 2 3 1 0 -5 2 6 4 1 0 36 -2 9 12 5 1 0 -329 22 9 28 20 6 1 0 3655 -206 18 52 |
Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 |
Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A001093 | 0 1 2 9 28 65 126 217 344 513 730 1001 1332 1729 2198 2745 3376 4097 4914 5833 6860 8001 9262 10649 |
Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 2 2 -2 22 -206 2354 -31426 480806 -8299406 159611938 -3385048322 78494559158 -1975904172238 |
Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 9 9 18 -81 1053 -14418 225747 -3967461 77413482 -1661390271 38908697571 -987669951714 |
Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 9 52 400 3726 41209 525512 7601283 122898250 2196729106 43010133948 915436196701 |
Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 -1 0 1 -3 3 0 1 -6 15 -15 0 1 -10 45 -105 105 0 1 -15 105 -420 945 -945 0 1 -21 210 -1260 |
Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A132062 | 1 0 1 0 -1 1 0 3 -3 1 0 -15 15 -6 1 0 105 -105 45 -10 1 0 -945 945 -420 105 -15 1 0 10395 -10395 |
Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A122848 | 1 0 1 0 1 1 0 0 3 1 0 0 3 6 1 0 0 0 15 10 1 0 0 0 15 45 15 1 0 0 0 0 105 105 21 1 0 0 0 0 105 420 |
Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -2 1 1 1 -5 10 -5 -5 1 -9 36 -69 36 36 1 -14 91 -329 616 -329 -329 1 -20 190 -1070 |
Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 3 0 1 0 -15 0 -6 -5 0 105 0 45 35 36 0 -945 0 -420 -315 -330 -329 0 10395 0 4725 |
Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -3 0 1 -6 3 1 -10 15 0 1 -15 45 -15 1 -21 105 -105 0 1 -28 210 -420 105 1 -36 378 |
Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -6 9 0 1 -12 45 -60 0 1 -20 135 -420 525 0 1 -30 315 -1680 4725 -5670 0 1 -42 630 |
Inv:Rev | RowSum∑ k=0..n T(n, k) | A278990 | 1 1 0 1 -5 36 -329 3655 -47844 721315 -12310199 234615096 -4939227215 113836841041 -2850860253240 |
Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 4 16 151 1051 15331 152839 3025576 39325276 984099601 15778499881 477491822809 9107153044081 |
Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -1 -3 -21 -115 -1380 -11676 -200683 -2304261 -51635475 -749484505 -20717727096 -363654981768 |
Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A001464 | 1 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A003436 | 1 2 1 1 -4 31 -293 3326 -44189 673471 -11588884 222304897 -4704612119 108897613826 -2737023412199 |
Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 4 -26 221 -2339 29569 -434251 7260994 -136133504 2827691351 -64444568891 1598655001789 |
Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 30 630 3780 207900 8108100 56756700 1929727800 329983453800 549972423000 139143023019000 |
Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
Inv:Rev | RowMaxMax k=0..n | T(n, k) | | A001147 | 1 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -1 -3 15 45 -420 -1260 17325 51975 -945945 -2837835 64324260 192972780 -5237832600 -15713497800 |
Inv:Rev | CentralET(2 n, n) | A376872 | 1 -1 15 -420 17325 -945945 64324260 -5237832600 496939367925 -53835098191875 6557114959770375 |
Inv:Rev | CentralOT(2 n + 1, n) | A245066 | 1 -3 45 -1260 51975 -2837835 192972780 -15713497800 1490818103775 -161505294575625 |
Inv:Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Inv:Rev | ColRightT(n, n) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -1 1 7 -124 1591 -19991 256691 -3335228 41759236 -430787224 595905949 182463444151 |
Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -19 175 -2076 29911 -505093 9757539 -211883500 5102919316 -134868653976 3878398876573 |
Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A006199 | 0 0 -1 3 -21 185 -2010 25914 -386407 6539679 -123823305 2593076255 -59505341676 1484818160748 |
Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 4 -26 221 -2339 29569 -434251 7260994 -136133504 2827691351 -64444568891 1598655001789 |
Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 9 -81 905 -11880 179424 -3065671 58474359 -1231741215 28400736815 -711483334056 |
Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 2 2 -2 22 -206 2354 -31426 480806 -8299406 159611938 -3385048322 78494559158 -1975904172238 |
Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A107104 | 1 -2 6 -26 154 -1182 11254 -128522 1715802 -26251118 453132214 -8714516538 184817376154 |
Inv:Rev | DiagRow1T(n + 1, n) | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
Inv:Rev | DiagRow2T(n + 2, n) | A001147 | 1 -3 15 -105 945 -10395 135135 -2027025 34459425 -654729075 13749310575 -316234143225 7905853580625 |
Inv:Rev | DiagRow3T(n + 3, n) | A001879 | 1 -6 45 -420 4725 -62370 945945 -16216200 310134825 -6547290750 151242416325 -3794809718700 |
Inv:Rev | DiagCol1T(n + 1, 1) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
Inv:Rev | DiagCol2T(n + 2, 2) | A050534 | 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
Inv:Rev | DiagCol3T(n + 3, 3) | A240440 | 0 -15 -105 -420 -1260 -3150 -6930 -13860 -25740 -45045 -75075 -120120 -185640 -278460 -406980 |
Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 1 -1 1 1 1 -5 7 -2 1 1 1 36 -71 19 -3 1 1 1 -329 1001 -287 37 -4 1 1 1 3655 |
Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A003215 | 1 1 7 19 37 61 91 127 169 217 271 331 397 469 547 631 721 817 919 1027 1141 1261 1387 1519 1657 |
Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A002119 | 1 1 -1 7 -71 1001 -18089 398959 -10391023 312129649 -10622799089 403978495031 -16977719590391 |
Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A065923 | 1 1 -2 19 -287 6046 -163529 5402503 -210861146 9494154073 -484412718869 27621019129606 |
Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -1 19 -743 53576 -6210629 1059175279 -249948171871 78048672688027 -31171008031911449 |
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Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.