BELL[0] 1
[1] 1, 2
[2] 2, 3, 5
[3] 5, 7, 10, 15
[4] 15, 20, 27, 37, 52
[5] 52, 67, 87, 114, 151, 203

      OEIS Similars: A011971, A011972, A123346

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA0119711 1 2 2 3 5 5 7 10 15 15 20 27 37 52 52 67 87 114 151 203 203 255 322 409 523 674 877 877 1080 1335
StdRevT(n, n - k), 0 ≤ k ≤ nA1233461 2 1 5 3 2 15 10 7 5 52 37 27 20 15 203 151 114 87 67 52 877 674 523 409 322 255 203 4140 3263
StdAccsee docsmissing1 1 3 2 5 10 5 12 22 37 15 35 62 99 151 52 119 206 320 471 674 203 458 780 1189 1712 2386 3263 877
StdAccRevsee docsmissing1 2 3 5 8 10 15 25 32 37 52 89 116 136 151 203 354 468 555 622 674 877 1551 2074 2483 2805 3060
StdAntiDiagsee docsmissing1 1 2 2 5 3 15 7 5 52 20 10 203 67 27 15 877 255 87 37 4140 1080 322 114 52 21147 5017 1335 409 151
StdDiffx1T(n, k) (k+1)missing1 1 4 2 6 15 5 14 30 60 15 40 81 148 260 52 134 261 456 755 1218 203 510 966 1636 2615 4044 6139
StdRowSum k=0..n T(n, k)A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
StdEvenSum k=0..n T(n, k) even(k)missing1 1 7 15 94 290 1925 7541 54217 254189 1979704 10725568 90086877 550986173 4964577987 33710074835
StdOddSum k=0..n T(n, k) odd(k)missing0 2 3 22 57 384 1338 9466 40611 308406 1555323 12705272 73168008 641073050 4132605615 38674652822
StdAltSum k=0..n T(n, k) (-1)^kA3677751 -1 4 -7 37 -94 587 -1925 13606 -54217 424381 -1979704 16918869 -90086877 831972372 -4964577987
StdAbsSum k=0..n | T(n, k) |A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
StdDiagSum k=0..n // 2 T(n - k, k)missing1 1 4 8 27 82 312 1256 5708 28059 149742 856168 5219507 33719235 229838064 1646511704 12356491915
StdAccSum k=0..n j=0..k T(n, j)A1243251 4 17 76 362 1842 9991 57568 351125 2259302 15288000 108478124 805037105 6233693772 50257390937
StdAccRevSum k=0..n j=0..k T(n, n - j)A2786771 5 23 109 544 2876 16113 95495 597155 3929243 27132324 196122796 1480531285 11647194573
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 210 259740 6087317964 150538831664272170 9345270808867942826280
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 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
StdRowMaxMax k=0..n | T(n, k) |A0001101 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
StdColMiddleT(n, n // 2)A2160781 1 3 7 27 87 409 1657 9089 43833 272947 1515903 10515147 65766991 501178937 3473600465 28773452321
StdCentralET(2 n, n)A0945771 3 27 409 9089 272947 10515147 501178937 28773452321 1949230218691 153281759047387
StdCentralOT(2 n + 1, n)A0205561 7 87 1657 43833 1515903 65766991 3473600465 218310229201 16035686850327 1356791248984295
StdColLeftT(n, 0)A0001101 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
StdColRightT(n, n)A0001101 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
StdBinConv k=0..n C(n, k) T(n, k)A1263901 3 13 71 457 3355 27509 248127 2434129 25741939 291397789 3510328695 44782460313 602513988107
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^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
StdTransNat0 k=0..n T(n, k) kmissing0 2 13 72 393 2202 12850 78488 502327 3366648 23597297 172691956 1317276400 10455135350 86200363093
StdTransNat1 k=0..n T(n, k) (k + 1)A2786771 5 23 109 544 2876 16113 95495 597155 3929243 27132324 196122796 1480531285 11647194573
StdTransSqrs k=0..n T(n, k) k^2missing0 2 23 182 1293 8932 62014 439442 3202127 24081458 187213595 1505287416 12516129504 107565432914
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA3678081 4 19 103 634 4393 33893 288158 2674849 26888251 290614732 3356438587 41203019361 535141595208
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA3678091 0 7 -17 166 -931 8333 -67902 668341 -6733957 74909152 -875130273 10931723505 -143624036492
StdDiagRow1T(n + 1, n)A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
StdDiagRow2T(n + 2, n)A0119652 7 27 114 523 2589 13744 77821 467767 2972432 19895813 139824045 1028804338 7905124379 63287544055
StdDiagRow3T(n + 3, n)A0119665 20 87 409 2066 11155 64077 389946 2504665 16923381 119928232 888980293 6876320041 55382419676
StdDiagCol1T(n + 1, 1)A0119682 3 7 20 67 255 1080 5017 25287 137122 794545 4892167 31858034 218543759 1573857867 11863100692
StdDiagCol2T(n + 2, 2)A0119695 10 27 87 322 1335 6097 30304 162409 931667 5686712 36750201 250401793 1792401626 13436958559
StdDiagCol3T(n + 3, 3)A01197015 37 114 409 1657 7432 36401 192713 1094076 6618379 42436913 287151994 2042803419 15229360185
StdPolysee docsmissing1 1 1 2 3 1 5 10 5 1 15 37 28 7 1 52 151 179 56 9 1 203 674 1291 521 94 11 1 877 3263 10358 5529
StdPolyRow1 k=0..1 T(1, k) n^kA0054081 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69
StdPolyRow2 k=0..2 T(2, k) n^kmissing2 10 28 56 94 142 200 268 346 434 532 640 758 886 1024 1172 1330 1498 1676 1864 2062 2270 2488 2716
StdPolyRow3 k=0..3 T(3, k) n^kmissing5 37 179 521 1153 2165 3647 5689 8381 11813 16075 21257 27449 34741 43223 52985 64117 76709 90851
StdPolyCol2 k=0..n T(n, k) 2^kA0956761 5 28 179 1291 10358 91337 876289 9070546 100596161 1188403063 14881408616 196696197075
StdPolyCol3 k=0..n T(n, k) 3^kmissing1 7 56 521 5529 65674 860387 12290251 189680754 3139572183 55393903633 1036547906904 20482256898421
StdPolyDiag k=0..n T(n, k) n^kmissing1 3 28 521 16207 745562 46937813 3842472699 394463953204 49422836065443 7399326825281095
AltTriangleT(n, k), 0 ≤ k ≤ nA0119711 1 -2 2 -3 5 5 -7 10 -15 15 -20 27 -37 52 52 -67 87 -114 151 -203 203 -255 322 -409 523 -674 877
AltRevT(n, n - k), 0 ≤ k ≤ nA1233461 -2 1 5 -3 2 -15 10 -7 5 52 -37 27 -20 15 -203 151 -114 87 -67 52 877 -674 523 -409 322 -255 203
AltAccsee docsmissing1 1 -1 2 -1 4 5 -2 8 -7 15 -5 22 -15 37 52 -15 72 -42 109 -94 203 -52 270 -139 384 -290 587 877
AltAccRevsee docsmissing1 -2 -1 5 2 4 -15 -5 -12 -7 52 15 42 22 37 -203 -52 -166 -79 -146 -94 877 203 726 317 639 384 587
AltAntiDiagsee docsmissing1 1 2 -2 5 -3 15 -7 5 52 -20 10 203 -67 27 -15 877 -255 87 -37 4140 -1080 322 -114 52 21147 -5017
AltDiffx1T(n, k) (k+1)missing1 1 -4 2 -6 15 5 -14 30 -60 15 -40 81 -148 260 52 -134 261 -456 755 -1218 203 -510 966 -1636 2615
AltRowSum k=0..n T(n, k)A3677751 -1 4 -7 37 -94 587 -1925 13606 -54217 424381 -1979704 16918869 -90086877 831972372 -4964577987
AltEvenSum k=0..n T(n, k) even(k)missing1 1 7 15 94 290 1925 7541 54217 254189 1979704 10725568 90086877 550986173 4964577987 33710074835
AltOddSum k=0..n T(n, k) odd(k)missing0 -2 -3 -22 -57 -384 -1338 -9466 -40611 -308406 -1555323 -12705272 -73168008 -641073050 -4132605615
AltAltSum k=0..n T(n, k) (-1)^kA0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
AltAbsSum k=0..n | T(n, k) |A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
AltDiagSum k=0..n // 2 T(n - k, k)missing1 1 0 2 13 42 148 672 3320 17207 95448 565712 3552437 23527165 163819720 1195607520 9120714907
AltAccSum k=0..n j=0..k T(n, j)missing1 0 5 4 54 82 963 2064 24401 66426 816840 2673148 34511241 131212000 1782125101 7690316816
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -3 11 -39 168 -740 3733 -19389 111659 -662813 4275732 -28409300 202352925 -1482515155 11529432851
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 210 259740 6087317964 150538831664272170 9345270808867942826280
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 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
AltRowMaxMax k=0..n | T(n, k) |A0001101 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
AltColMiddleT(n, n // 2)A2160781 1 -3 -7 27 87 -409 -1657 9089 43833 -272947 -1515903 10515147 65766991 -501178937 -3473600465
AltCentralET(2 n, n)A0945771 -3 27 -409 9089 -272947 10515147 -501178937 28773452321 -1949230218691 153281759047387
AltCentralOT(2 n + 1, n)A0205561 -7 87 -1657 43833 -1515903 65766991 -3473600465 218310229201 -16035686850327 1356791248984295
AltColLeftT(n, 0)A0001101 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
AltColRightT(n, n)A0001101 -2 5 -15 52 -203 877 -4140 21147 -115975 678570 -4213597 27644437 -190899322 1382958545
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA1263901 -3 13 -71 457 -3355 27509 -248127 2434129 -25741939 291397789 -3510328695 44782460313
AltTransNat0 k=0..n T(n, k) kmissing0 -2 7 -32 131 -646 3146 -17464 98053 -608596 3851351 -26429596 185434056 -1392428278 10697460479
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -3 11 -39 168 -740 3733 -19389 111659 -662813 4275732 -28409300 202352925 -1482515155 11529432851
AltTransSqrs k=0..n T(n, k) k^2missing0 -2 17 -102 587 -3404 20442 -127714 833881 -5684842 40468069 -300257112 2319609440 -18624360050
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA3678091 0 7 17 166 931 8333 67902 668341 6733957 74909152 875130273 10931723505 143624036492
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA3678081 -4 19 -103 634 -4393 33893 -288158 2674849 -26888251 290614732 -3356438587 41203019361
AltDiagRow1T(n + 1, n)A0054931 -3 10 -37 151 -674 3263 -17007 94828 -562595 3535027 -23430840 163254885 -1192059223 9097183602
AltDiagRow2T(n + 2, n)A0119652 -7 27 -114 523 -2589 13744 -77821 467767 -2972432 19895813 -139824045 1028804338 -7905124379
AltDiagRow3T(n + 3, n)A0119665 -20 87 -409 2066 -11155 64077 -389946 2504665 -16923381 119928232 -888980293 6876320041
AltDiagCol1T(n + 1, 1)A011968-2 -3 -7 -20 -67 -255 -1080 -5017 -25287 -137122 -794545 -4892167 -31858034 -218543759 -1573857867
AltDiagCol2T(n + 2, 2)A0119695 10 27 87 322 1335 6097 30304 162409 931667 5686712 36750201 250401793 1792401626 13436958559
AltDiagCol3T(n + 3, 3)A011970-15 -37 -114 -409 -1657 -7432 -36401 -192713 -1094076 -6618379 -42436913 -287151994 -2042803419
AltPolysee docsmissing1 1 1 2 -1 1 5 4 -3 1 15 -7 16 -5 1 52 37 -89 38 -7 1 203 -94 619 -331 70 -9 1 877 587 -4726 3411
AltPolyRow1 k=0..1 T(1, k) n^kA0054081 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49
AltPolyRow2 k=0..2 T(2, k) n^kmissing2 4 16 38 70 112 164 226 298 380 472 574 686 808 940 1082 1234 1396 1568 1750 1942 2144 2356 2578
AltPolyRow3 k=0..3 T(3, k) n^kmissing5 -7 -89 -331 -823 -1655 -2917 -4699 -7091 -10183 -14065 -18827 -24559 -31351 -39293 -48475 -58987
AltPolyCol2 k=0..n T(n, k) 2^kmissing1 -3 16 -89 619 -4726 40637 -380079 3863854 -42154987 491379103 -6080324316 79542696711
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -5 38 -331 3411 -39542 509207 -7172321 109439376 -1794126189 31397283583 -583367343864
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 16 -331 11311 -552358 36276017 -3064641809 322392680356 -41190080729385 6266282927712655
RevTriangleT(n, k), 0 ≤ k ≤ nA1233461 2 1 5 3 2 15 10 7 5 52 37 27 20 15 203 151 114 87 67 52 877 674 523 409 322 255 203 4140 3263
RevAccsee docsmissing1 2 3 5 8 10 15 25 32 37 52 89 116 136 151 203 354 468 555 622 674 877 1551 2074 2483 2805 3060
RevAccRevsee docsmissing1 1 3 2 5 10 5 12 22 37 15 35 62 99 151 52 119 206 320 471 674 203 458 780 1189 1712 2386 3263 877
RevAntiDiagsee docsmissing1 2 5 1 15 3 52 10 2 203 37 7 877 151 27 5 4140 674 114 20 21147 3263 523 87 15 115975 17007 2589
RevDiffx1T(n, k) (k+1)missing1 2 2 5 6 6 15 20 21 20 52 74 81 80 75 203 302 342 348 335 312 877 1348 1569 1636 1610 1530 1421
RevRowSum k=0..n T(n, k)A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
RevEvenSum k=0..n T(n, k) even(k)missing1 2 7 22 94 384 1925 9466 54217 308406 1979704 12705272 90086877 641073050 4964577987 38674652822
RevOddSum k=0..n T(n, k) odd(k)missing0 1 3 15 57 290 1338 7541 40611 254189 1555323 10725568 73168008 550986173 4132605615 33710074835
RevAltSum k=0..n T(n, k) (-1)^kA3677751 1 4 7 37 94 587 1925 13606 54217 424381 1979704 16918869 90086877 831972372 4964577987
RevAbsSum k=0..n | T(n, k) |A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
RevDiagSum k=0..n // 2 T(n - k, k)missing1 2 6 18 64 247 1060 4948 25035 136047 789582 4867080 31721935 217753974 1568990584 11831377880
RevAccSum k=0..n j=0..k T(n, j)A2786771 5 23 109 544 2876 16113 95495 597155 3929243 27132324 196122796 1480531285 11647194573
RevAccRevSum k=0..n j=0..k T(n, n - j)A1243251 4 17 76 362 1842 9991 57568 351125 2259302 15288000 108478124 805037105 6233693772 50257390937
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 30 210 259740 6087317964 150538831664272170 9345270808867942826280
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 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
RevRowMaxMax k=0..n | T(n, k) |A0001101 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
RevColMiddleT(n, n // 2)A2163321 2 3 10 27 114 409 2066 9089 52922 272947 1788850 10515147 76282138 501178937 3974779402
RevCentralET(2 n, n)A0945771 3 27 409 9089 272947 10515147 501178937 28773452321 1949230218691 153281759047387
RevCentralOT(2 n + 1, n)A2087822 10 114 2066 52922 1788850 76282138 3974779402 247083681522 17984917069018 1510073008031682
RevColLeftT(n, 0)A0001101 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
RevColRightT(n, n)A0001101 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147
RevBinConv k=0..n C(n, k) T(n, k)A1263901 3 13 71 457 3355 27509 248127 2434129 25741939 291397789 3510328695 44782460313 602513988107
RevTransNat0 k=0..n T(n, k) kA0929230 1 7 39 211 1168 6728 40561 256297 1696707 11752973 85047284 641782220 5041634549 41160207335
RevTransNat1 k=0..n T(n, k) (k + 1)A1243251 4 17 76 362 1842 9991 57568 351125 2259302 15288000 108478124 805037105 6233693772 50257390937
RevTransSqrs k=0..n T(n, k) k^2missing0 1 11 83 565 3762 25282 173953 1233887 9051989 68770355 541196024 4410199344 37189922501
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0956761 5 28 179 1291 10358 91337 876289 9070546 100596161 1188403063 14881408616 196696197075
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -3 16 -89 619 -4726 40637 -380079 3863854 -42154987 491379103 -6080324316 79542696711
RevDiagRow1T(n + 1, n)A0119682 3 7 20 67 255 1080 5017 25287 137122 794545 4892167 31858034 218543759 1573857867 11863100692
RevDiagRow2T(n + 2, n)A0119695 10 27 87 322 1335 6097 30304 162409 931667 5686712 36750201 250401793 1792401626 13436958559
RevDiagRow3T(n + 3, n)A01197015 37 114 409 1657 7432 36401 192713 1094076 6618379 42436913 287151994 2042803419 15229360185
RevDiagCol1T(n + 1, 1)A0054931 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602
RevDiagCol2T(n + 2, 2)A0119652 7 27 114 523 2589 13744 77821 467767 2972432 19895813 139824045 1028804338 7905124379 63287544055
RevDiagCol3T(n + 3, 3)A0119665 20 87 409 2066 11155 64077 389946 2504665 16923381 119928232 888980293 6876320041 55382419676
RevPolysee docsmissing1 2 1 5 3 1 15 10 4 1 52 37 19 5 1 203 151 103 32 6 1 877 674 634 243 49 7 1 4140 3263 4393 2161
RevPolyRow1 k=0..1 T(1, k) n^kA0000272 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 37
RevPolyRow2 k=0..2 T(2, k) n^kmissing5 10 19 32 49 70 95 124 157 194 235 280 329 382 439 500 565 634 707 784 865 950 1039 1132 1229 1330
RevPolyRow3 k=0..3 T(3, k) n^kmissing15 37 103 243 487 865 1407 2143 3103 4317 5815 7627 9783 12313 15247 18615 22447 26773 31623 37027
RevPolyCol2 k=0..n T(n, k) 2^kA3678081 4 19 103 634 4393 33893 288158 2674849 26888251 290614732 3356438587 41203019361 535141595208
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 5 32 243 2161 22094 254683 3256953 45618666 692724613 11311059297 197274441832 3654815145445
RevPolyDiag k=0..n T(n, k) n^kmissing1 3 19 243 5752 219058 11983453 876586413 81864886291 9448581092347 1315300140417220
 << 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.