BINOMIALPELL[0] 1
[1] 2, 2
[2] 5, 6, 3
[3] 12, 20, 12, 4
[4] 29, 60, 50, 20, 5
[5] 70, 174, 180, 100, 30, 6

      OEIS Similars: A367211

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA3672111 2 2 5 6 3 12 20 12 4 29 60 50 20 5 70 174 180 100 30 6 169 490 609 420 175 42 7 408 1352 1960
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 2 2 3 6 5 4 12 20 12 5 20 50 60 29 6 30 100 180 174 70 7 42 175 420 609 490 169 8 56 280 840 1624
StdAccsee docsmissing1 2 4 5 11 14 12 32 44 48 29 89 139 159 164 70 244 424 524 554 560 169 659 1268 1688 1863 1905 1912
StdAccRevsee docsmissing1 2 4 3 9 14 4 16 36 48 5 25 75 135 164 6 36 136 316 490 560 7 49 224 644 1253 1743 1912 8 64 344
StdAntiDiagsee docsmissing1 2 5 2 12 6 29 20 3 70 60 12 169 174 50 4 408 490 180 20 985 1352 609 100 5 2378 3672 1960 420 30
StdDiffx1T(n, k) (k+1)missing1 2 4 5 12 9 12 40 36 16 29 120 150 80 25 70 348 540 400 150 36 169 980 1827 1680 875 252 49 408
StdRowSum k=0..n T(n, k)A0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
StdEvenSum k=0..n T(n, k) even(k)A0940381 2 8 24 84 280 960 3264 11152 38048 129920 443520 1514304 5170048 17651712 60266496 205762816
StdOddSum k=0..n T(n, k) odd(k)missing0 2 6 24 80 280 952 3264 11136 38048 129888 443520 1514240 5170048 17651584 60266496 205762560
StdAltSum k=0..n T(n, k) (-1)^kA0779571 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536
StdAbsSum k=0..n | T(n, k) |A0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
StdDiagSum k=0..n // 2 T(n - k, k)A0996261 2 7 18 52 142 397 1098 3051 8460 23480 65140 180749 501498 1391483 3860822 10712348 29722698
StdAccSum k=0..n j=0..k T(n, j)missing1 6 30 136 580 2376 9464 36928 141840 538080 2020832 7526784 27839552 102361728 374448000
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 6 26 104 404 1544 5832 21824 81040 298976 1096864 4004736 14560064 52739712 190404736 685385728
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 60 8700 182700 72044700 489903960 868599721080 178062942821400 3748284300704743800
StdRowGcdGcd k=0..n | T(n, k) | > 1A0065191 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 32 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16
StdRowMaxMax k=0..n | T(n, k) |missing1 2 6 20 60 180 609 1960 6084 20280 67320 216700 704275 2380378 7836465 25225200 85765680 286693848
StdColMiddleT(n, n // 2)missing1 2 6 20 50 180 420 1624 3654 14700 32340 133848 290004 1225224 2625480 11268400 23945350 104056524
StdCentralET(2 n, n)missing1 6 50 420 3654 32340 290004 2625480 23945350 219674884 2024942556 18739801080 174007238300
StdCentralOT(2 n + 1, n)missing2 20 180 1624 14700 133848 1225224 11268400 104056524 964258360 8962513560 83523474384 780168321400
StdColLeftT(n, 0)A0001291 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
StdColRightT(n, n)A0000271 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
StdBinConv k=0..n C(n, k) T(n, k)missing1 4 20 112 654 3896 23528 143552 882790 5462616 33971992 212147552 1329423692 8355515312
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 0 -4 16 14 -144 344 832 -5018 6560 40072 -165472 50764 1731744 -5051216 -4502272 69147654
StdTransNat0 k=0..n T(n, k) kmissing0 2 12 56 240 984 3920 15296 58752 222880 837056 3117696 11531520 42399616 155101440 564852736
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 6 26 104 404 1544 5832 21824 81040 298976 1096864 4004736 14560064 52739712 190404736 685385728
StdTransSqrs k=0..n T(n, k) k^2missing0 2 18 104 520 2424 10808 46656 196416 810400 3288736 13162368 52061568 203840896 791095680
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA0011091 6 35 204 1189 6930 40391 235416 1372105 7997214 46611179 271669860 1583407981 9228778026
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0155191 -2 11 -36 149 -550 2143 -8136 31273 -119498 457907 -1752300 6709949 -25685998 98341639 -376485264
StdDiagRow1T(n + 1, n)A0023782 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
StdDiagRow2T(n + 2, n)A1344815 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120
StdDiagRow3T(n + 3, n)A03348612 60 180 420 840 1512 2520 3960 5940 8580 12012 16380 21840 28560 36720 46512 58140 71820 87780
StdDiagCol1T(n + 1, 1)A3617322 6 20 60 174 490 1352 3672 9850 26158 68892 180180 468454 1211730 3120400 8004144 20460402
StdDiagCol2T(n + 2, 2)missing3 12 50 180 609 1960 6084 18360 54175 156948 447798 1261260 3513405 9693840 26523400 72037296
StdDiagCol3T(n + 3, 3)missing4 20 100 420 1624 5880 20280 67320 216700 680108 2089724 6306300 18738160 54931760 159140400
StdPolysee docsmissing1 2 1 5 4 1 12 14 6 1 29 48 29 8 1 70 164 132 50 10 1 169 560 589 288 77 12 1 408 1912 2610 1604
StdPolyRow1 k=0..1 T(1, k) n^kA0058432 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68
StdPolyRow2 k=0..2 T(2, k) n^kA0059185 14 29 50 77 110 149 194 245 302 365 434 509 590 677 770 869 974 1085 1202 1325 1454 1589 1730
StdPolyRow3 k=0..3 T(3, k) n^kA29202212 48 132 288 540 912 1428 2112 2988 4080 5412 7008 8892 11088 13620 16512 19788 23472 27588 32160
StdPolyCol2 k=0..n T(n, k) 2^kA0811791 6 29 132 589 2610 11537 50952 224953 993054 4383653 19350540 85417669 377052234 1664389721
StdPolyCol3 k=0..n T(n, k) 3^kA0811801 8 50 288 1604 8800 47944 260352 1411600 7647872 41420576 224294400 1214467136 6575615488
StdPolyDiag k=0..n T(n, k) n^kmissing1 4 29 288 3629 55440 995737 20562432 480032665 12501761600 359362704821 11301501657600
AltTriangleT(n, k), 0 ≤ k ≤ nA3672111 2 -2 5 -6 3 12 -20 12 -4 29 -60 50 -20 5 70 -174 180 -100 30 -6 169 -490 609 -420 175 -42 7 408
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -2 2 3 -6 5 -4 12 -20 12 5 -20 50 -60 29 -6 30 -100 180 -174 70 7 -42 175 -420 609 -490 169 -8 56
AltAccsee docsmissing1 2 0 5 -1 2 12 -8 4 0 29 -31 19 -1 4 70 -104 76 -24 6 0 169 -321 288 -132 43 1 8 408 -944 1016
AltAccRevsee docsmissing1 -2 0 3 -3 2 -4 8 -12 0 5 -15 35 -25 4 -6 24 -76 104 -70 0 7 -35 140 -280 329 -161 8 -8 48 -232
AltAntiDiagsee docsmissing1 2 5 -2 12 -6 29 -20 3 70 -60 12 169 -174 50 -4 408 -490 180 -20 985 -1352 609 -100 5 2378 -3672
AltDiffx1T(n, k) (k+1)missing1 2 -4 5 -12 9 12 -40 36 -16 29 -120 150 -80 25 70 -348 540 -400 150 -36 169 -980 1827 -1680 875
AltRowSum k=0..n T(n, k)A0779571 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536
AltEvenSum k=0..n T(n, k) even(k)A0940381 2 8 24 84 280 960 3264 11152 38048 129920 443520 1514304 5170048 17651712 60266496 205762816
AltOddSum k=0..n T(n, k) odd(k)missing0 -2 -6 -24 -80 -280 -952 -3264 -11136 -38048 -129888 -443520 -1514240 -5170048 -17651584 -60266496
AltAltSum k=0..n T(n, k) (-1)^kA0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
AltAbsSum k=0..n | T(n, k) |A0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
AltDiagSum k=0..n // 2 T(n - k, k)A1125751 2 3 6 12 22 41 78 147 276 520 980 1845 3474 6543 12322 23204 43698 82293 154974 291847 549608
AltAccSum k=0..n j=0..k T(n, j)A0939681 2 6 8 20 24 56 64 144 160 352 384 832 896 1920 2048 4352 4608 9728 10240 21504 22528 47104 49152
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -2 2 -8 4 -24 8 -64 16 -160 32 -384 64 -896 128 -2048 256 -4608 512 -10240 1024 -22528 2048
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 60 8700 182700 72044700 489903960 868599721080 178062942821400 3748284300704743800
AltRowGcdGcd k=0..n | T(n, k) | > 1A0065191 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 32 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16
AltRowMaxMax k=0..n | T(n, k) |missing1 2 6 20 60 180 609 1960 6084 20280 67320 216700 704275 2380378 7836465 25225200 85765680 286693848
AltColMiddleT(n, n // 2)missing1 2 -6 -20 50 180 -420 -1624 3654 14700 -32340 -133848 290004 1225224 -2625480 -11268400 23945350
AltCentralET(2 n, n)missing1 -6 50 -420 3654 -32340 290004 -2625480 23945350 -219674884 2024942556 -18739801080 174007238300
AltCentralOT(2 n + 1, n)missing2 -20 180 -1624 14700 -133848 1225224 -11268400 104056524 -964258360 8962513560 -83523474384
AltColLeftT(n, 0)A0001291 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
AltColRightT(n, n)A0000271 -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
AltBinConv k=0..n C(n, k) T(n, k)missing1 0 -4 -16 14 144 344 -832 -5018 -6560 40072 165472 50764 -1731744 -5051216 4502272 69147654
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -4 20 -112 654 -3896 23528 -143552 882790 -5462616 33971992 -212147552 1329423692 -8355515312
AltTransNat0 k=0..n T(n, k) kA0362890 -2 0 -8 0 -24 0 -64 0 -160 0 -384 0 -896 0 -2048 0 -4608 0 -10240 0 -22528 0 -49152 0 -106496 0
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -2 2 -8 4 -24 8 -64 16 -160 32 -384 64 -896 128 -2048 256 -4608 512 -10240 1024 -22528 2048
AltTransSqrs k=0..n T(n, k) k^2missing0 -2 6 -8 40 -24 168 -64 576 -160 1760 -384 4992 -896 13440 -2048 34816 -4608 87552 -10240 215040
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0155191 2 11 36 149 550 2143 8136 31273 119498 457907 1752300 6709949 25685998 98341639 376485264
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0011091 -6 35 -204 1189 -6930 40391 -235416 1372105 -7997214 46611179 -271669860 1583407981 -9228778026
AltDiagRow1T(n + 1, n)A0023782 -6 12 -20 30 -42 56 -72 90 -110 132 -156 182 -210 240 -272 306 -342 380 -420 462 -506 552 -600
AltDiagRow2T(n + 2, n)A1344815 -20 50 -100 175 -280 420 -600 825 -1100 1430 -1820 2275 -2800 3400 -4080 4845 -5700 6650 -7700
AltDiagRow3T(n + 3, n)A03348612 -60 180 -420 840 -1512 2520 -3960 5940 -8580 12012 -16380 21840 -28560 36720 -46512 58140 -71820
AltDiagCol1T(n + 1, 1)A361732-2 -6 -20 -60 -174 -490 -1352 -3672 -9850 -26158 -68892 -180180 -468454 -1211730 -3120400 -8004144
AltDiagCol2T(n + 2, 2)missing3 12 50 180 609 1960 6084 18360 54175 156948 447798 1261260 3513405 9693840 26523400 72037296
AltDiagCol3T(n + 3, 3)missing-4 -20 -100 -420 -1624 -5880 -20280 -67320 -216700 -680108 -2089724 -6306300 -18738160 -54931760
AltPolysee docsmissing1 2 1 5 0 1 12 2 -2 1 29 0 5 -4 1 70 4 -12 14 -6 1 169 0 29 -48 29 -8 1 408 8 -70 164 -132 50 -10 1
AltPolyRow1 k=0..1 T(1, k) n^kA0058432 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50
AltPolyRow2 k=0..2 T(2, k) n^kA0059185 2 5 14 29 50 77 110 149 194 245 302 365 434 509 590 677 770 869 974 1085 1202 1325 1454 1589 1730
AltPolyRow3 k=0..3 T(3, k) n^kA29202212 0 -12 -48 -132 -288 -540 -912 -1428 -2112 -2988 -4080 -5412 -7008 -8892 -11088 -13620 -16512
AltPolyCol2 k=0..n T(n, k) 2^kA0001291 -2 5 -12 29 -70 169 -408 985 -2378 5741 -13860 33461 -80782 195025 -470832 1136689 -2744210
AltPolyCol3 k=0..n T(n, k) 3^kA0070701 -4 14 -48 164 -560 1912 -6528 22288 -76096 259808 -887040 3028544 -10340096 35303296 -120532992
AltPolyDiag k=0..n T(n, k) n^kmissing1 0 5 -48 589 -8800 155233 -3159168 72872473 -1879016704 53559541661 -1672317123840 56763783073061
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 2 2 3 6 5 4 12 20 12 5 20 50 60 29 6 30 100 180 174 70 7 42 175 420 609 490 169 8 56 280 840 1624
RevAccsee docsmissing1 2 4 3 9 14 4 16 36 48 5 25 75 135 164 6 36 136 316 490 560 7 49 224 644 1253 1743 1912 8 64 344
RevAccRevsee docsmissing1 2 4 5 11 14 12 32 44 48 29 89 139 159 164 70 244 424 524 554 560 169 659 1268 1688 1863 1905 1912
RevAntiDiagsee docsmissing1 2 3 2 4 6 5 12 5 6 20 20 7 30 50 12 8 42 100 60 9 56 175 180 29 10 72 280 420 174 11 90 420 840
RevDiffx1T(n, k) (k+1)missing1 2 4 3 12 15 4 24 60 48 5 40 150 240 145 6 60 300 720 870 420 7 84 525 1680 3045 2940 1183 8 112
RevRowSum k=0..n T(n, k)A0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
RevEvenSum k=0..n T(n, k) even(k)A0940381 2 8 24 84 280 960 3264 11152 38048 129920 443520 1514304 5170048 17651712 60266496 205762816
RevOddSum k=0..n T(n, k) odd(k)missing0 2 6 24 80 280 952 3264 11136 38048 129888 443520 1514240 5170048 17651584 60266496 205762560
RevAltSum k=0..n T(n, k) (-1)^kA0779571 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536
RevAbsSum k=0..n | T(n, k) |A0070701 4 14 48 164 560 1912 6528 22288 76096 259808 887040 3028544 10340096 35303296 120532992 411525376
RevDiagSum k=0..n // 2 T(n - k, k)missing1 2 5 10 22 46 99 210 449 956 2040 4348 9273 19770 42157 89886 191662 408666 871379 1857986 3961681
RevAccSum k=0..n j=0..k T(n, j)missing1 6 26 104 404 1544 5832 21824 81040 298976 1096864 4004736 14560064 52739712 190404736 685385728
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 6 30 136 580 2376 9464 36928 141840 538080 2020832 7526784 27839552 102361728 374448000
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 60 8700 182700 72044700 489903960 868599721080 178062942821400 3748284300704743800
RevRowGcdGcd k=0..n | T(n, k) | > 1A0065191 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 32 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16
RevRowMaxMax k=0..n | T(n, k) |missing1 2 6 20 60 180 609 1960 6084 20280 67320 216700 704275 2380378 7836465 25225200 85765680 286693848
RevColMiddleT(n, n // 2)missing1 2 6 12 50 100 420 840 3654 7308 32340 64680 290004 580008 2625480 5250960 23945350 47890700
RevCentralET(2 n, n)missing1 6 50 420 3654 32340 290004 2625480 23945350 219674884 2024942556 18739801080 174007238300
RevCentralOT(2 n + 1, n)missing2 12 100 840 7308 64680 580008 5250960 47890700 439349768 4049885112 37479602160 348014476600
RevColLeftT(n, 0)A0000271 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
RevColRightT(n, n)A0001291 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
RevBinConv k=0..n C(n, k) T(n, k)missing1 4 20 112 654 3896 23528 143552 882790 5462616 33971992 212147552 1329423692 8355515312
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 0 -4 -16 14 144 344 -832 -5018 -6560 40072 165472 50764 -1731744 -5051216 4502272 69147654
RevTransNat0 k=0..n T(n, k) kmissing0 2 16 88 416 1816 7552 30400 119552 461984 1761024 6639744 24811008 92021632 339144704 1243142144
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 6 30 136 580 2376 9464 36928 141840 538080 2020832 7526784 27839552 102361728 374448000
RevTransSqrs k=0..n T(n, k) k^2missing0 2 26 200 1224 6584 32600 152384 682816 2962336 12528416 51904896 211415424 848927104 3367701376
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0811791 6 29 132 589 2610 11537 50952 224953 993054 4383653 19350540 85417669 377052234 1664389721
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0001291 -2 5 -12 29 -70 169 -408 985 -2378 5741 -13860 33461 -80782 195025 -470832 1136689 -2744210
RevDiagRow1T(n + 1, n)A3617322 6 20 60 174 490 1352 3672 9850 26158 68892 180180 468454 1211730 3120400 8004144 20460402
RevDiagRow2T(n + 2, n)missing3 12 50 180 609 1960 6084 18360 54175 156948 447798 1261260 3513405 9693840 26523400 72037296
RevDiagRow3T(n + 3, n)missing4 20 100 420 1624 5880 20280 67320 216700 680108 2089724 6306300 18738160 54931760 159140400
RevDiagCol1T(n + 1, 1)A0023782 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
RevDiagCol2T(n + 2, 2)A1344815 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120
RevDiagCol3T(n + 3, 3)A03348612 60 180 420 840 1512 2520 3960 5940 8580 12012 16380 21840 28560 36720 46512 58140 71820 87780
RevPolysee docsmissing1 2 1 3 4 1 4 14 6 1 5 48 35 8 1 6 164 204 66 10 1 7 560 1189 544 107 12 1 8 1912 6930 4484 1140
RevPolyRow1 k=0..1 T(1, k) n^kA0058432 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68
RevPolyRow2 k=0..2 T(2, k) n^kmissing3 14 35 66 107 158 219 290 371 462 563 674 795 926 1067 1218 1379 1550 1731 1922 2123 2334 2555
RevPolyRow3 k=0..3 T(3, k) n^kmissing4 48 204 544 1140 2064 3388 5184 7524 10480 14124 18528 23764 29904 37020 45184 54468 64944 76684
RevPolyCol2 k=0..n T(n, k) 2^kA0011091 6 35 204 1189 6930 40391 235416 1372105 7997214 46611179 271669860 1583407981 9228778026
RevPolyCol3 k=0..n T(n, k) 3^kA1903311 8 66 544 4484 36960 304648 2511104 20698128 170607232 1406254112 11591247360 95542487104
RevPolyDiag k=0..n T(n, k) n^kmissing1 4 35 544 12149 352656 12581647 532210176 26029628233 1444806913600 89717842023611
 << 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.