WARDSET[0] 1
[1] 0, 1
[2] 0, 1, 3
[3] 0, 1, 10, 15
[4] 0, 1, 25, 105, 105
[5] 0, 1, 56, 490, 1260, 945

      OEIS Similars: A269939, A134991

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA2699391 0 1 0 1 3 0 1 10 15 0 1 25 105 105 0 1 56 490 1260 945 0 1 119 1918 9450 17325 10395 0 1 246 6825
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 3 1 0 15 10 1 0 105 105 25 1 0 945 1260 490 56 1 0 10395 17325 9450 1918 119 1 0 135135
StdAccsee docsmissing1 0 1 0 1 4 0 1 11 26 0 1 26 131 236 0 1 57 547 1807 2752 0 1 120 2038 11488 28813 39208 0 1 247
StdAccRevsee docsmissing1 1 1 3 4 4 15 25 26 26 105 210 235 236 236 945 2205 2695 2751 2752 2752 10395 27720 37170 39088
StdAntiDiagsee docsA1373751 0 0 1 0 1 0 1 3 0 1 10 0 1 25 15 0 1 56 105 0 1 119 490 105 0 1 246 1918 1260 0 1 501 6825 9450
StdDiffx1T(n, k) (k+1)missing1 0 2 0 2 9 0 2 30 60 0 2 75 420 525 0 2 168 1960 6300 5670 0 2 357 7672 47250 103950 72765 0 2 738
StdRowSum k=0..n T(n, k)A0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
StdEvenSum k=0..n T(n, k) even(k)missing1 0 3 10 130 1316 19964 327496 6429616 140887472 3471763328 94313132992 2808914011072
StdOddSum k=0..n T(n, k) odd(k)missing0 1 1 16 106 1436 19244 332536 6389296 141250352 3468134528 94353049792 2808435009472
StdAltSum k=0..n T(n, k) (-1)^kA0001421 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200
StdAbsSum k=0..n | T(n, k) |A0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
StdDiagSum k=0..n // 2 T(n - k, k)A0002961 0 1 1 4 11 41 162 715 3425 17722 98253 580317 3633280 24011157 166888165 1216070380 9264071767
StdAccSum k=0..n j=0..k T(n, j)missing1 1 5 38 394 5164 81668 1510928 31986400 762118432 20175223232 587316779840 18642954295744
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 2 11 92 1022 14100 231996 4429360 96202720 2341397632 63103551040 1865343596352 59999931991872
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 3 30 525 52920 242099550 45099954900 367310208815775225 127007737277649228000
StdRowGcdGcd k=0..n | T(n, k) | > 1A1105601 1 3 5 5 7 7 1 1 11 11 13 13 1 1 17 17 19 19 1 1 23 23 1 1 1 1 29 29 31 31 1 1 1 1 37 37 1 1 41 41
StdRowMaxMax k=0..n | T(n, k) |missing1 1 3 15 105 1260 17325 270270 4729725 94594500 2343240900 62199262125 1764494857125 53338158823950
StdColMiddleT(n, n // 2)missing1 0 1 1 25 56 1918 6825 302995 1487200 81431350 510880370 33309926650 254752658160 19282395272140
StdCentralET(2 n, n)missing1 1 25 1918 302995 81431350 33309926650 19282395272140 15006064187108995 15112611709896650950
StdCentralOT(2 n + 1, n)missing0 1 56 6825 1487200 510880370 254752658160 174073797222325 156226380361251200 178278935386370568750
StdColLeftT(n, 0)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
StdColRightT(n, n)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
StdBinConv k=0..n C(n, k) T(n, k)missing1 1 5 48 679 12710 296246 8267448 268799091 9978566310 416461324630 19303231146496 983832736305574
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 1 -12 -169 -1010 11614 484736 7251635 -31586634 -5267648770 -152227865064 -803876214010
StdTransNat0 k=0..n T(n, k) kmissing0 1 7 66 786 11348 192788 3769328 83383808 2059259808 56163653184 1676677413568 54382582971328
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 2 11 92 1022 14100 231996 4429360 96202720 2341397632 63103551040 1865343596352 59999931991872
StdTransSqrs k=0..n T(n, k) k^2missing0 1 13 176 2726 48420 976284 22089800 555025760 15345208528 463187349472 15160891200768
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 1 5 39 423 5889 100125 2010951 46589967 1223110881 35883307125 1163450728359 41312822139063
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0016621 1 1 -1 -13 -47 73 2447 16811 -15551 -1726511 -18994849 -10979677 2983409137 48421103257
StdDiagRow1T(n + 1, n)A0004570 1 10 105 1260 17325 270270 4729725 91891800 1964187225 45831035250 1159525191825 31623414322500
StdDiagRow2T(n + 2, n)A0004970 1 25 490 9450 190575 4099095 94594500 2343240900 62199262125 1764494857125 53338158823950
StdDiagRow3T(n + 3, n)A0005040 1 56 1918 56980 1636635 47507460 1422280860 44346982680 1446733012725 49473074851200
StdDiagCol1T(n + 1, 1)A0000121 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
StdDiagCol2T(n + 2, 2)A0002473 10 25 56 119 246 501 1012 2035 4082 8177 16368 32751 65518 131053 262124 524267 1048554 2097129
StdDiagCol3T(n + 3, 3)A00047815 105 490 1918 6825 22935 74316 235092 731731 2252341 6879678 20900922 63259533 190957923
StdPolysee docsmissing1 0 1 0 1 1 0 4 2 1 0 26 14 3 1 0 236 162 30 4 1 0 2752 2622 498 52 5 1 0 39208 54546 11568 1124 80
StdPolyRow1 k=0..1 T(1, k) n^kA0000270 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
StdPolyRow2 k=0..2 T(2, k) n^kA0494510 4 14 30 52 80 114 154 200 252 310 374 444 520 602 690 784 884 990 1102 1220 1344 1474 1610 1752
StdPolyRow3 k=0..3 T(3, k) n^kmissing0 26 162 498 1124 2130 3606 5642 8328 11754 16010 21186 27372 34658 43134 52890 64016 76602 90738
StdPolyCol2 k=0..n T(n, k) 2^kA2014651 2 14 162 2622 54546 1386702 41660226 1444071006 56728401138 2490626473326 120858220146978
StdPolyCol3 k=0..n T(n, k) 3^kA2014661 3 30 498 11568 345432 12606240 543678672 27054328512 1525746223488 96167433279360
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 14 498 34004 3803280 632374098 146428634576 45056223763272 17784343544317920
AltTriangleT(n, k), 0 ≤ k ≤ nA2699391 0 -1 0 -1 3 0 -1 10 -15 0 -1 25 -105 105 0 -1 56 -490 1260 -945 0 -1 119 -1918 9450 -17325 10395
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -1 0 3 -1 0 -15 10 -1 0 105 -105 25 -1 0 -945 1260 -490 56 -1 0 10395 -17325 9450 -1918 119 -1 0
AltAccsee docsmissing1 0 -1 0 -1 2 0 -1 9 -6 0 -1 24 -81 24 0 -1 55 -435 825 -120 0 -1 118 -1800 7650 -9675 720 0 -1 245
AltAccRevsee docsmissing1 -1 -1 3 2 2 -15 -5 -6 -6 105 0 25 24 24 -945 315 -175 -119 -120 -120 10395 -6930 2520 602 721 720
AltAntiDiagsee docsA1373751 0 0 -1 0 -1 0 -1 3 0 -1 10 0 -1 25 -15 0 -1 56 -105 0 -1 119 -490 105 0 -1 246 -1918 1260 0 -1
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -2 9 0 -2 30 -60 0 -2 75 -420 525 0 -2 168 -1960 6300 -5670 0 -2 357 -7672 47250 -103950
AltRowSum k=0..n T(n, k)A0001421 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200
AltEvenSum k=0..n T(n, k) even(k)missing1 0 3 10 130 1316 19964 327496 6429616 140887472 3471763328 94313132992 2808914011072
AltOddSum k=0..n T(n, k) odd(k)missing0 -1 -1 -16 -106 -1436 -19244 -332536 -6389296 -141250352 -3468134528 -94353049792 -2808435009472
AltAltSum k=0..n T(n, k) (-1)^kA0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
AltAbsSum k=0..n | T(n, k) |A0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
AltDiagSum k=0..n // 2 T(n - k, k)A0005871 0 -1 -1 2 9 9 -50 -267 -413 2180 17731 50533 -110176 -1966797 -9938669 -8638718 278475061
AltAccSum k=0..n j=0..k T(n, j)A3236181 -1 1 2 -34 324 -2988 28944 -300816 3371040 -40710240 528439680 -7348717440 109109064960
AltAccRevSum k=0..n j=0..k T(n, n - j)A1215551 -2 7 -32 178 -1164 8748 -74304 704016 -7362720 84255840 -1047358080 14054739840 -202514376960
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 3 30 525 52920 242099550 45099954900 367310208815775225 127007737277649228000
AltRowGcdGcd k=0..n | T(n, k) | > 1A1105601 1 3 5 5 7 7 1 1 11 11 13 13 1 1 17 17 19 19 1 1 23 23 1 1 1 1 29 29 31 31 1 1 1 1 37 37 1 1 41 41
AltRowMaxMax k=0..n | T(n, k) |missing1 1 3 15 105 1260 17325 270270 4729725 94594500 2343240900 62199262125 1764494857125 53338158823950
AltColMiddleT(n, n // 2)missing1 0 -1 -1 25 56 -1918 -6825 302995 1487200 -81431350 -510880370 33309926650 254752658160
AltCentralET(2 n, n)missing1 -1 25 -1918 302995 -81431350 33309926650 -19282395272140 15006064187108995 -15112611709896650950
AltCentralOT(2 n + 1, n)missing0 -1 56 -6825 1487200 -510880370 254752658160 -174073797222325 156226380361251200
AltColLeftT(n, 0)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AltColRightT(n, n)A0011471 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225
AltBinConv k=0..n C(n, k) T(n, k)missing1 -1 1 12 -169 1010 11614 -484736 7251635 31586634 -5267648770 152227865064 -803876214010
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 5 -48 679 -12710 296246 -8267448 268799091 -9978566310 416461324630 -19303231146496
AltTransNat0 k=0..n T(n, k) kA0017050 -1 5 -26 154 -1044 8028 -69264 663696 -6999840 80627040 -1007441280 13575738240 -196287356160
AltTransNat1 k=0..n T(n, k) (k + 1)A1215551 -2 7 -32 178 -1164 8748 -74304 704016 -7362720 84255840 -1047358080 14054739840 -202514376960
AltTransSqrs k=0..n T(n, k) k^2missing0 -1 11 -96 834 -7652 75508 -805032 9268128 -114922512 1529695584 -21780381312 330590371968
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0016621 -1 1 1 -13 47 73 -2447 16811 15551 -1726511 18994849 -10979677 -2983409137 48421103257
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -1 5 -39 423 -5889 100125 -2010951 46589967 -1223110881 35883307125 -1163450728359 41312822139063
AltDiagRow1T(n + 1, n)A0004570 -1 10 -105 1260 -17325 270270 -4729725 91891800 -1964187225 45831035250 -1159525191825
AltDiagRow2T(n + 2, n)A0004970 -1 25 -490 9450 -190575 4099095 -94594500 2343240900 -62199262125 1764494857125 -53338158823950
AltDiagRow3T(n + 3, n)A0005040 -1 56 -1918 56980 -1636635 47507460 -1422280860 44346982680 -1446733012725 49473074851200
AltDiagCol1T(n + 1, 1)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
AltDiagCol2T(n + 2, 2)A0002473 10 25 56 119 246 501 1012 2035 4082 8177 16368 32751 65518 131053 262124 524267 1048554 2097129
AltDiagCol3T(n + 3, 3)A000478-15 -105 -490 -1918 -6825 -22935 -74316 -235092 -731731 -2252341 -6879678 -20900922 -63259533
AltPolysee docsmissing1 0 1 0 -1 1 0 2 -2 1 0 -6 10 -3 1 0 24 -82 24 -4 1 0 -120 938 -318 44 -5 1 0 720 -13778 5892 -804
AltPolyRow1 k=0..1 T(1, k) n^kA0000270 -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
AltPolyRow2 k=0..2 T(2, k) n^kA0494500 2 10 24 44 70 102 140 184 234 290 352 420 494 574 660 752 850 954 1064 1180 1302 1430 1564 1704
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 -6 -82 -318 -804 -1630 -2886 -4662 -7048 -10134 -14010 -18766 -24492 -31278 -39214 -48390 -58896
AltPolyCol2 k=0..n T(n, k) 2^kA1124871 -2 10 -82 938 -13778 247210 -5240338 128149802 -3551246162 109979486890 -3764281873042
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -3 24 -318 5892 -140304 4082712 -140389824 5569868256 -250435202592 12584594167296
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 10 -318 20556 -2225480 362107110 -82561002048 25111037280056 -9822547851440256
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 3 1 0 15 10 1 0 105 105 25 1 0 945 1260 490 56 1 0 10395 17325 9450 1918 119 1 0 135135
RevAccsee docsmissing1 1 1 3 4 4 15 25 26 26 105 210 235 236 236 945 2205 2695 2751 2752 2752 10395 27720 37170 39088
RevAccRevsee docsmissing1 0 1 0 1 4 0 1 11 26 0 1 26 131 236 0 1 57 547 1807 2752 0 1 120 2038 11488 28813 39208 0 1 247
RevAntiDiagsee docsmissing1 1 3 0 15 1 105 10 0 945 105 1 10395 1260 25 0 135135 17325 490 1 2027025 270270 9450 56 0
RevDiffx1T(n, k) (k+1)missing1 1 0 3 2 0 15 20 3 0 105 210 75 4 0 945 2520 1470 224 5 0 10395 34650 28350 7672 595 6 0 135135
RevRowSum k=0..n T(n, k)A0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
RevEvenSum k=0..n T(n, k) even(k)missing1 1 3 16 130 1436 19964 332536 6429616 141250352 3471763328 94353049792 2808914011072
RevOddSum k=0..n T(n, k) odd(k)missing0 0 1 10 106 1316 19244 327496 6389296 140887472 3468134528 94313132992 2808435009472
RevAltSum k=0..n T(n, k) (-1)^kA0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
RevAbsSum k=0..n | T(n, k) |A0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 3 16 115 1051 11680 152951 2306801 39381644 750777069 15809735761 364456230076 9129012460481
RevAccSum k=0..n j=0..k T(n, j)missing1 2 11 92 1022 14100 231996 4429360 96202720 2341397632 63103551040 1865343596352 59999931991872
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 1 5 38 394 5164 81668 1510928 31986400 762118432 20175223232 587316779840 18642954295744
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 3 30 525 52920 242099550 45099954900 367310208815775225 127007737277649228000
RevRowGcdGcd k=0..n | T(n, k) | > 1A1105601 1 3 5 5 7 7 1 1 11 11 13 13 1 1 17 17 19 19 1 1 23 23 1 1 1 1 29 29 31 31 1 1 1 1 37 37 1 1 41 41
RevRowMaxMax k=0..n | T(n, k) |missing1 1 3 15 105 1260 17325 270270 4729725 94594500 2343240900 62199262125 1764494857125 53338158823950
RevColMiddleT(n, n // 2)missing1 1 1 10 25 490 1918 56980 302995 12122110 81431350 4104160060 33309926650 2026763158420
RevCentralET(2 n, n)missing1 1 25 1918 302995 81431350 33309926650 19282395272140 15006064187108995 15112611709896650950
RevCentralOT(2 n + 1, n)missing1 10 490 56980 12122110 4104160060 2026763158420 1375295856374440 1227858424500457750
RevColLeftT(n, 0)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
RevColRightT(n, n)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
RevBinConv k=0..n C(n, k) T(n, k)missing1 1 5 48 679 12710 296246 8267448 268799091 9978566310 416461324630 19303231146496 983832736305574
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 1 12 -169 1010 11614 -484736 7251635 31586634 -5267648770 152227865064 -803876214010
RevTransNat0 k=0..n T(n, k) kmissing0 0 1 12 158 2412 42460 850896 19167488 479980608 13235325376 398650597056 13025605275200
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 1 5 38 394 5164 81668 1510928 31986400 762118432 20175223232 587316779840 18642954295744
RevTransSqrs k=0..n T(n, k) k^2missing0 0 1 14 214 3740 74316 1660776 41295200 1131695728 33904071392 1102596219136 38689467601152
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA2014651 2 14 162 2622 54546 1386702 41660226 1444071006 56728401138 2490626473326 120858220146978
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA1124871 -2 10 -82 938 -13778 247210 -5240338 128149802 -3551246162 109979486890 -3764281873042
RevDiagRow1T(n + 1, n)A0000121 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
RevDiagRow2T(n + 2, n)A0002473 10 25 56 119 246 501 1012 2035 4082 8177 16368 32751 65518 131053 262124 524267 1048554 2097129
RevDiagRow3T(n + 3, n)A00047815 105 490 1918 6825 22935 74316 235092 731731 2252341 6879678 20900922 63259533 190957923
RevDiagCol1T(n + 1, 1)A0004570 1 10 105 1260 17325 270270 4729725 91891800 1964187225 45831035250 1159525191825 31623414322500
RevDiagCol2T(n + 2, 2)A0004970 1 25 490 9450 190575 4099095 94594500 2343240900 62199262125 1764494857125 53338158823950
RevDiagCol3T(n + 3, 3)A0005040 1 56 1918 56980 1636635 47507460 1422280860 44346982680 1446733012725 49473074851200
RevPolysee docsmissing1 1 1 3 1 1 15 4 1 1 105 26 5 1 1 945 236 39 6 1 1 10395 2752 423 54 7 1 1 135135 39208 5889 672 71
RevPolyRow1 k=0..1 T(1, k) n^kA0000121 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
RevPolyRow2 k=0..2 T(2, k) n^kA0000273 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 37
RevPolyRow3 k=0..3 T(3, k) n^kmissing15 26 39 54 71 90 111 134 159 186 215 246 279 314 351 390 431 474 519 566 615 666 719 774 831 890
RevPolyCol2 k=0..n T(n, k) 2^kmissing1 1 5 39 423 5889 100125 2010951 46589967 1223110881 35883307125 1163450728359 41312822139063
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 1 6 54 672 10728 209088 4812912 127780416 3843863424 129211334784 4800040010496 195279931289088
RevPolyDiag k=0..n T(n, k) n^kmissing1 1 5 54 989 27120 1030833 51548336 3266196921 254885395680 23959128651325 2664724081561344
 << TableSourceSimilarsIndex >> 

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.