EULERIAN2[0] 1
[1] 0, 1
[2] 0, 1, 2
[3] 0, 1, 8, 6
[4] 0, 1, 22, 58, 24
[5] 0, 1, 52, 328, 444, 120

      OEIS Similars: A340556, A008517, A112007, A163936

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA2016371 0 1 0 1 2 0 1 8 6 0 1 22 58 24 0 1 52 328 444 120 0 1 114 1452 4400 3708 720 0 1 240 5610 32120
StdRevT(n, n - k), 0 ≤ k ≤ nA1639361 1 0 2 1 0 6 8 1 0 24 58 22 1 0 120 444 328 52 1 0 720 3708 4400 1452 114 1 0 5040 33984 58140
StdAccsee docsmissing1 0 1 0 1 3 0 1 9 15 0 1 23 81 105 0 1 53 381 825 945 0 1 115 1567 5967 9675 10395 0 1 241 5851
StdAccRevsee docsmissing1 1 1 2 3 3 6 14 15 15 24 82 104 105 105 120 564 892 944 945 945 720 4428 8828 10280 10394 10395
StdAntiDiagsee docsmissing1 0 0 1 0 1 0 1 2 0 1 8 0 1 22 6 0 1 52 58 0 1 114 328 24 0 1 240 1452 444 0 1 494 5610 4400 120 0
StdDiffx1T(n, k) (k+1)missing1 0 2 0 2 6 0 2 24 24 0 2 66 232 120 0 2 156 1312 2220 720 0 2 342 5808 22000 22248 5040 0 2 720
StdRowSum k=0..n T(n, k)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
StdEvenSum k=0..n T(n, k) even(k)missing1 0 2 8 46 496 5234 66344 1021918 17237488 326501282 6884152712 158111581774 3951435085744
StdOddSum k=0..n T(n, k) odd(k)missing0 1 1 7 59 449 5161 68791 1005107 17221937 328227793 6865157863 158122561451 3954418494881
StdAltSum k=0..n T(n, k) (-1)^kA0016621 -1 1 1 -13 47 73 -2447 16811 15551 -1726511 18994849 -10979677 -2983409137 48421103257
StdAbsSum k=0..n | T(n, k) |A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
StdDiagSum k=0..n // 2 T(n - k, k)missing1 0 1 1 3 9 29 111 467 2137 10625 56783 323947 1963425 12585209 84977087 602402531 4470338673
StdAccSum k=0..n j=0..k T(n, j)A2618981 1 4 25 210 2205 27720 405405 6756750 126351225 2618916300 59580345825 1475759335050
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 2 8 50 420 4410 55440 810810 13513500 252702450 5237832600 119160691650 2951518670100
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 24 7656 2366520 852469200 308503863360 240006609023406825600 8842151410302701559591432000000
StdRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2
StdRowMaxMax k=0..n | T(n, k) |A0073471 1 2 8 58 444 4400 58140 785304 12440064 238904904 4642163952 101180433024 2549865473424
StdColMiddleT(n, n // 2)missing1 0 1 1 22 52 1452 5610 195800 1062500 44765000 314369720 15548960784 134323420224 7634832149392
StdCentralET(2 n, n)A3673691 1 22 1452 195800 44765000 15548960784 7634832149392 5036317938475648 4297211671488276816
StdCentralOT(2 n + 1, n)missing0 1 52 5610 1062500 314369720 134323420224 78391384831312 59958264360283168 58222825873768855728
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)A0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
StdBinConv k=0..n C(n, k) T(n, k)missing1 1 4 33 392 6145 119724 2789465 75660080 2341894185 81464695900 3146287488729 133588851589368
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 0 -15 -80 665 17136 55209 -4162752 -83069415 626654600 62101020553 812999167344 -36896508029199
StdTransNat0 k=0..n T(n, k) kA0515770 1 5 35 315 3465 45045 675675 11486475 218243025 4583103525 105411381075 2635284526875
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 2 8 50 420 4410 55440 810810 13513500 252702450 5237832600 119160691650 2951518670100
StdTransSqrs k=0..n T(n, k) k^2missing0 1 9 87 995 13265 202545 3489255 66981915 1418241825 32839832025 825613363575 22397626926675
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA3411061 1 0 -6 -12 144 1080 -5184 -127008 -95904 19077120 154929024 -3210337152 -70284900096 391453171200
StdDiagRow1T(n + 1, n)A0025380 1 8 58 444 3708 33984 341136 3733920 44339040 568356480 7827719040 115336085760 1810992556800
StdDiagRow2T(n + 2, n)A0025390 1 22 328 4400 58140 785304 11026296 162186912 2507481216 40788301824 697929436800 12550904017920
StdDiagRow3T(n + 3, n)A1120080 1 52 1452 32120 644020 12440064 238904904 4642163952 92199790224 1883079661824 39689578055808
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)A0058032 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738 65504 131038 262108 524250 1048536 2097110
StdDiagCol3T(n + 3, 3)A0043016 58 328 1452 5610 19950 67260 218848 695038 2170626 6699696 20507988 62407890 189123286 571432036
StdPolysee docsmissing1 0 1 0 1 1 0 3 2 1 0 15 10 3 1 0 105 82 21 4 1 0 945 938 237 36 5 1 0 10395 13778 3711 516 55 6 1
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^kA0141050 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275
StdPolyRow3 k=0..3 T(3, k) n^kmissing0 15 82 237 516 955 1590 2457 3592 5031 6810 8965 11532 14547 18046 22065 26640 31807 37602 44061
StdPolyCol2 k=0..n T(n, k) 2^kA1124871 2 10 82 938 13778 247210 5240338 128149802 3551246162 109979486890 3764281873042 141104799067178
StdPolyCol3 k=0..n T(n, k) 3^kmissing1 3 21 237 3711 74451 1822557 52680189 1755990327 66313036227 2798166464229 130478035336653
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 10 237 10212 694805 68445870 9205055433 1619649615752 361017218715561 99394667604650610
AltTriangleT(n, k), 0 ≤ k ≤ nA2016371 0 -1 0 -1 2 0 -1 8 -6 0 -1 22 -58 24 0 -1 52 -328 444 -120 0 -1 114 -1452 4400 -3708 720 0 -1 240
AltRevT(n, n - k), 0 ≤ k ≤ nA1639361 -1 0 2 -1 0 -6 8 -1 0 24 -58 22 -1 0 -120 444 -328 52 -1 0 720 -3708 4400 -1452 114 -1 0 -5040
AltAccsee docsmissing1 0 -1 0 -1 1 0 -1 7 1 0 -1 21 -37 -13 0 -1 51 -277 167 47 0 -1 113 -1339 3061 -647 73 0 -1 239
AltAccRevsee docsmissing1 -1 -1 2 1 1 -6 2 1 1 24 -34 -12 -13 -13 -120 324 -4 48 47 47 720 -2988 1412 -40 74 73 73 -5040
AltAntiDiagsee docsmissing1 0 0 -1 0 -1 0 -1 2 0 -1 8 0 -1 22 -6 0 -1 52 -58 0 -1 114 -328 24 0 -1 240 -1452 444 0 -1 494
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -2 6 0 -2 24 -24 0 -2 66 -232 120 0 -2 156 -1312 2220 -720 0 -2 342 -5808 22000 -22248
AltRowSum k=0..n T(n, k)A0016621 -1 1 1 -13 47 73 -2447 16811 15551 -1726511 18994849 -10979677 -2983409137 48421103257
AltEvenSum k=0..n T(n, k) even(k)missing1 0 2 8 46 496 5234 66344 1021918 17237488 326501282 6884152712 158111581774 3951435085744
AltOddSum k=0..n T(n, k) odd(k)missing0 -1 -1 -7 -59 -449 -5161 -68791 -1005107 -17221937 -328227793 -6865157863 -158122561451
AltAltSum k=0..n T(n, k) (-1)^kA0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
AltAbsSum k=0..n | T(n, k) |A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
AltDiagSum k=0..n // 2 T(n - k, k)missing1 0 -1 -1 1 7 15 -7 -191 -769 -837 9465 73145 237687 -345949 -9576439 -61788895 -151452665
AltAccSum k=0..n j=0..k T(n, j)missing1 -1 0 7 -30 -13 1260 -9629 630 871031 -10360680 14987263 1486214730 -25702256197 91711734660
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -2 4 -2 -48 342 -676 -12394 167480 -699970 -10357452 231945774 -1639930208 -19048880858
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 24 7656 2366520 852469200 308503863360 240006609023406825600 8842151410302701559591432000000
AltRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2
AltRowMaxMax k=0..n | T(n, k) |A0073471 1 2 8 58 444 4400 58140 785304 12440064 238904904 4642163952 101180433024 2549865473424
AltColMiddleT(n, n // 2)missing1 0 -1 -1 22 52 -1452 -5610 195800 1062500 -44765000 -314369720 15548960784 134323420224
AltCentralET(2 n, n)A3673691 -1 22 -1452 195800 -44765000 15548960784 -7634832149392 5036317938475648 -4297211671488276816
AltCentralOT(2 n + 1, n)missing0 -1 52 -5610 1062500 -314369720 134323420224 -78391384831312 59958264360283168
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)A0001421 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200
AltBinConv k=0..n C(n, k) T(n, k)missing1 -1 0 15 -80 -665 17136 -55209 -4162752 83069415 626654600 -62101020553 812999167344
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 4 -33 392 -6145 119724 -2789465 75660080 -2341894185 81464695900 -3146287488729
AltTransNat0 k=0..n T(n, k) kmissing0 -1 3 -3 -35 295 -749 -9947 150669 -715521 -8630941 212950925 -1628950531 -16065471721
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -2 4 -2 -48 342 -676 -12394 167480 -699970 -10357452 231945774 -1639930208 -19048880858
AltTransSqrs k=0..n T(n, k) k^2missing0 -1 7 -23 -51 1359 -8993 -12647 990485 -10607425 2037687 1746425673 -27717388195 68175251375
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA3411061 -1 0 6 -12 -144 1080 5184 -127008 95904 19077120 -154929024 -3210337152 70284900096 391453171200
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0003111 -1 4 -26 236 -2752 39208 -660032 12818912 -282137824 6939897856 -188666182784 5617349020544
AltDiagRow1T(n + 1, n)A0025380 -1 8 -58 444 -3708 33984 -341136 3733920 -44339040 568356480 -7827719040 115336085760
AltDiagRow2T(n + 2, n)A0025390 -1 22 -328 4400 -58140 785304 -11026296 162186912 -2507481216 40788301824 -697929436800
AltDiagRow3T(n + 3, n)A1120080 -1 52 -1452 32120 -644020 12440064 -238904904 4642163952 -92199790224 1883079661824
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)A0058032 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738 65504 131038 262108 524250 1048536 2097110
AltDiagCol3T(n + 3, 3)A004301-6 -58 -328 -1452 -5610 -19950 -67260 -218848 -695038 -2170626 -6699696 -20507988 -62407890
AltPolysee docsmissing1 0 1 0 -1 1 0 1 -2 1 0 1 6 -3 1 0 -13 -18 15 -4 1 0 47 6 -93 28 -5 1 0 73 846 573 -260 45 -6 1 0
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^kA0003840 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 1 -18 -93 -260 -555 -1014 -1673 -2568 -3735 -5210 -7029 -9228 -11843 -14910 -18465 -22544 -27183
AltPolyCol2 k=0..n T(n, k) 2^kmissing1 -2 6 -18 6 846 -13338 139374 -717498 -13142898 548192934 -11698830162 151948973574 415271462094
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -3 15 -93 573 -1587 -57945 2076243 -50209563 993218397 -14021842305 -34362482493 13772318432973
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 6 -93 2780 -137205 10151778 -1054424441 146594602872 -26314931370825 5929536086954590
RevTriangleT(n, k), 0 ≤ k ≤ nA1639361 1 0 2 1 0 6 8 1 0 24 58 22 1 0 120 444 328 52 1 0 720 3708 4400 1452 114 1 0 5040 33984 58140
RevAccsee docsmissing1 1 1 2 3 3 6 14 15 15 24 82 104 105 105 120 564 892 944 945 945 720 4428 8828 10280 10394 10395
RevAccRevsee docsmissing1 0 1 0 1 3 0 1 9 15 0 1 23 81 105 0 1 53 381 825 945 0 1 115 1567 5967 9675 10395 0 1 241 5851
RevAntiDiagsee docsmissing1 1 2 0 6 1 24 8 0 120 58 1 720 444 22 0 5040 3708 328 1 40320 33984 4400 52 0 362880 341136 58140
RevDiffx1T(n, k) (k+1)missing1 1 0 2 2 0 6 16 3 0 24 116 66 4 0 120 888 984 208 5 0 720 7416 13200 5808 570 6 0 5040 67968
RevRowSum k=0..n T(n, k)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
RevEvenSum k=0..n T(n, k) even(k)missing1 1 2 7 46 449 5234 68791 1021918 17221937 326501282 6865157863 158111581774 3954418494881
RevOddSum k=0..n T(n, k) odd(k)missing0 0 1 8 59 496 5161 66344 1005107 17237488 328227793 6884152712 158122561451 3951435085744
RevAltSum k=0..n T(n, k) (-1)^kA0016621 1 1 -1 -13 -47 73 2447 16811 -15551 -1726511 -18994849 -10979677 2983409137 48421103257
RevAbsSum k=0..n | T(n, k) |A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 2 7 32 179 1186 9077 78756 763609 8180258 95931767 1222181096 16806911411 248101263114
RevAccSum k=0..n j=0..k T(n, j)missing1 2 8 50 420 4410 55440 810810 13513500 252702450 5237832600 119160691650 2951518670100
RevAccRevSum k=0..n j=0..k T(n, n - j)A2618981 1 4 25 210 2205 27720 405405 6756750 126351225 2618916300 59580345825 1475759335050
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 24 7656 2366520 852469200 308503863360 240006609023406825600 8842151410302701559591432000000
RevRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 2
RevRowMaxMax k=0..n | T(n, k) |A0073471 1 2 8 58 444 4400 58140 785304 12440064 238904904 4642163952 101180433024 2549865473424
RevColMiddleT(n, n // 2)missing1 1 1 8 22 328 1452 32120 195800 5765500 44765000 1648384304 15548960784 687720046384 7634832149392
RevCentralET(2 n, n)A3673691 1 22 1452 195800 44765000 15548960784 7634832149392 5036317938475648 4297211671488276816
RevCentralOT(2 n + 1, n)missing1 8 328 32120 5765500 1648384304 687720046384 394365587815520 297593170417847920
RevColLeftT(n, 0)A0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
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 4 33 392 6145 119724 2789465 75660080 2341894185 81464695900 3146287488729 133588851589368
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 0 15 -80 -665 17136 -55209 -4162752 83069415 626654600 -62101020553 812999167344
RevTransNat0 k=0..n T(n, k) kA0004570 0 1 10 105 1260 17325 270270 4729725 91891800 1964187225 45831035250 1159525191825 31623414322500
RevTransNat1 k=0..n T(n, k) (k + 1)A2618981 1 4 25 210 2205 27720 405405 6756750 126351225 2618916300 59580345825 1475759335050
RevTransSqrs k=0..n T(n, k) k^2missing0 0 1 12 155 2240 36225 651420 12927915 281080800 6650669025 170229559500 4688514906075
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA1124871 2 10 82 938 13778 247210 5240338 128149802 3551246162 109979486890 3764281873042 141104799067178
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -2 6 -18 6 846 -13338 139374 -717498 -13142898 548192934 -11698830162 151948973574 415271462094
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)A0058032 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738 65504 131038 262108 524250 1048536 2097110
RevDiagRow3T(n + 3, n)A0043016 58 328 1452 5610 19950 67260 218848 695038 2170626 6699696 20507988 62407890 189123286 571432036
RevDiagCol1T(n + 1, 1)A0025380 1 8 58 444 3708 33984 341136 3733920 44339040 568356480 7827719040 115336085760 1810992556800
RevDiagCol2T(n + 2, 2)A0025390 1 22 328 4400 58140 785304 11026296 162186912 2507481216 40788301824 697929436800 12550904017920
RevDiagCol3T(n + 3, 3)A1120080 1 52 1452 32120 644020 12440064 238904904 4642163952 92199790224 1883079661824 39689578055808
RevPolysee docsmissing1 1 1 2 1 1 6 3 1 1 24 15 4 1 1 120 105 26 5 1 1 720 945 236 39 6 1 1 5040 10395 2752 423 54 7 1 1
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^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
RevPolyRow3 k=0..3 T(3, k) n^kmissing6 15 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^kA0003111 1 4 26 236 2752 39208 660032 12818912 282137824 6939897856 188666182784 5617349020544
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 1 5 39 423 5889 100125 2010951 46589967 1223110881 35883307125 1163450728359 41312822139063
RevPolyDiag k=0..n T(n, k) n^kmissing1 1 4 39 672 17665 650520 31729887 1970081792 151152782049 14003884454400 1538038294455575
 << 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.