cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A350264 a(n) = Sum_{k=0..n} BellPolynomial(n, k), row sums of A350263.

Original entry on oeis.org

1, 1, 8, 84, 1174, 20680, 440593, 11024076, 316969656, 10299839283, 373313501065, 14932585789000, 653449085198220, 31053925215635803, 1592721740865950464, 87690229418143373920, 5158511908430168388088, 322910810936913397280700, 21431596667884889101766973
Offset: 0

Views

Author

Peter Luschny, Dec 23 2021

Keywords

Crossrefs

Cf. A350263.

Programs

  • Mathematica
    Table[Sum[BellB[n, k], {k, 0, n}], {n, 0, 18}]

A350256 Triangle read by rows. T(n, k) = BellPolynomial(n, k).

Original entry on oeis.org

1, 0, 1, 0, 2, 6, 0, 5, 22, 57, 0, 15, 94, 309, 756, 0, 52, 454, 1866, 5428, 12880, 0, 203, 2430, 12351, 42356, 115155, 268098, 0, 877, 14214, 88563, 355636, 1101705, 2869242, 6593839, 0, 4140, 89918, 681870, 3188340, 11202680, 32510850, 82187658, 187104200
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle begins:
[0] 1
[1] 0,    1
[2] 0,    2,     6
[3] 0,    5,    22,     57
[4] 0,   15,    94,    309,     756
[5] 0,   52,   454,   1866,    5428,    12880
[6] 0,  203,  2430,  12351,   42356,   115155,   268098
[7] 0,  877, 14214,  88563,  355636,  1101705,  2869242,  6593839
[8] 0, 4140, 89918, 681870, 3188340, 11202680, 32510850, 82187658, 187104200

Crossrefs

Cf. A242817 (main diagonal), A000110 (column 1), A350264 (row sums), A350263 (Bell(n,-k)), A189233 and A292860 (array).

Programs

  • Maple
    A350256 := (n, k) -> ifelse(n = 0, 1, BellB(n, k)):
seq(seq(A350256(n, k), k = 0..n), n = 0..8);
  • Mathematica
    T[n_, k_] := BellB[n, k]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

A350257 Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, k).

Original entry on oeis.org

1, 0, 1, 0, 2, 24, 0, 5, 176, 1539, 0, 15, 1504, 25029, 193536, 0, 52, 14528, 453438, 5558272, 40250000, 0, 203, 155520, 9003879, 173490176, 1799296875, 12508380288, 0, 877, 1819392, 193687281, 5826740224, 86070703125, 803204128512, 5430309951577
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle starts:
[0] 1
[1] 0,   1
[2] 0,   2,      24
[3] 0,   5,     176,     1539
[4] 0,  15,    1504,    25029,     193536
[5] 0,  52,   14528,   453438,    5558272,    40250000
[6] 0, 203,  155520,  9003879,  173490176,  1799296875, 12508380288

Crossrefs

Cf. A350256, A350258, A350259, A350260, A350261, A350262, A350263.
Cf. A000110.

Programs

  • Maple
    A350257 := (n, k) -> ifelse(n = 0, 1, k^n * BellB(n, k)):
seq(seq(A350257(n, k), k = 0..n), n = 0..7);
  • Mathematica
    T[n_, k_] := k^n BellB[n, k]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten

A350258 Triangle read by rows. T(n, k) = k! * BellPolynomial(n, k).

Original entry on oeis.org

1, 0, 1, 0, 2, 12, 0, 5, 44, 342, 0, 15, 188, 1854, 18144, 0, 52, 908, 11196, 130272, 1545600, 0, 203, 4860, 74106, 1016544, 13818600, 193030560, 0, 877, 28428, 531378, 8535264, 132204600, 2065854240, 33232948560
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle starts:
[0] 1
[1] 0,   1
[2] 0,   2,    12
[3] 0,   5,    44,    342
[4] 0,  15,   188,   1854,   18144
[5] 0,  52,   908,  11196,  130272,   1545600
[6] 0, 203,  4860,  74106, 1016544,  13818600,  193030560
[7] 0, 877, 28428, 531378, 8535264, 132204600, 2065854240, 33232948560

Crossrefs

Cf. A350256, A350257, A350259, A350260, A350261, A350262, A350263.
Cf. A000110.

Programs

  • Maple
    A350258 := (n, k) -> ifelse(n = 0, 1, k! * BellB(n, k)):
seq(seq(A350258(n, k), k = 0..n), n = 0..7);
  • Mathematica
    T[n_, k_] := k! BellB[n, k]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten

A350259 Triangle read by rows. T(n, k) = n! * BellPolynomial(n, k).

Original entry on oeis.org

1, 0, 1, 0, 4, 12, 0, 30, 132, 342, 0, 360, 2256, 7416, 18144, 0, 6240, 54480, 223920, 651360, 1545600, 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560, 0, 4420080, 71638560, 446357520, 1792405440, 5552593200, 14460979680, 33232948560
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle starts:
[0] 1
[1] 0,      1
[2] 0,      4,      12
[3] 0,     30,     132,     342
[4] 0,    360,    2256,    7416,    18144
[5] 0,   6240,   54480,  223920,   651360,  1545600
[6] 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560

Crossrefs

Cf. A350256, A350257, A350258, A350260, A350261, A350262, A350263.
Cf. A000110, A137341.

Programs

  • Maple
    A350259 := (n, k) -> ifelse(n = 0, 1, n! * BellB(n, k)):
seq(seq(A350259(n, k), k = 0..n), n = 0..7);
  • Mathematica
    T[n_, k_] := n! BellB[n, k]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

A350260 Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, 1/k) for k > 0, if k = 0 then T(n, k) = k^n.

Original entry on oeis.org

1, 0, 1, 0, 2, 3, 0, 5, 11, 19, 0, 15, 49, 109, 201, 0, 52, 257, 742, 1657, 3176, 0, 203, 1539, 5815, 15821, 35451, 69823, 0, 877, 10299, 51193, 170389, 447981, 1007407, 2026249, 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle starts:
[0] 1
[1] 0,    1
[2] 0,    2,     3
[3] 0,    5,    11,     19
[4] 0,   15,    49,    109,     201
[5] 0,   52,   257,    742,    1657,    3176
[6] 0,  203,  1539,   5815,   15821,   35451,    69823
[7] 0,  877, 10299,  51193,  170389,  447981,  1007407,  2026249
[8] 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473

Crossrefs

Cf. A350256, A350257, A350258, A350259, A350261, A350262, A350263.
Cf. A000110, A301419.

Programs

  • Maple
    A350260 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, 1/k)):
seq(seq(A350260(n, k), k = 0..n), n = 0..8);
  • Mathematica
    T[n_, k_] := If[k == 0, k^n, k^n BellB[n, 1/k]];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

A350261 Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then T(n, k) = k^n.

Original entry on oeis.org

1, 0, -1, 0, 0, -1, 0, 1, 1, -1, 0, 1, 9, 19, 25, 0, -2, 23, 128, 343, 674, 0, -9, -25, 379, 2133, 6551, 15211, 0, -9, -583, -1549, 3603, 33479, 123821, 331827, 0, 50, -3087, -32600, -112975, -174114, 120865, 1619108, 5987745
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			Triangle starts:
[0] 1
[1] 0, -1
[2] 0,  0,    -1
[3] 0,  1,     1,     -1
[4] 0,  1,     9,     19,      25
[5] 0, -2,    23,    128,     343,     674
[6] 0, -9,   -25,    379,    2133,    6551,  15211
[7] 0, -9,  -583,  -1549,    3603,   33479, 123821,  331827
[8] 0, 50, -3087, -32600, -112975, -174114, 120865, 1619108, 5987745

Crossrefs

Cf. A350256, A350257, A350258, A350259, A350260, A350262, A350263.
Cf. A000587, A318183.

Programs

  • Maple
    A350261 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
seq(seq(A350261(n, k), k = 0..n), n = 0..8);
  • Mathematica
    T[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

A350262 Triangle read by rows. T(n, k) = B(n, n - k + 1) where B(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then B(n, k) = k^n.

Original entry on oeis.org

1, -1, -1, -2, -1, 0, -5, -1, 1, 1, 21, 25, 19, 9, 1, 1103, 674, 343, 128, 23, -2, 29835, 15211, 6551, 2133, 379, -25, -9, 739751, 331827, 123821, 33479, 3603, -1549, -583, -9, 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
Offset: 0

Views

Author

Peter Luschny, Dec 22 2021

Keywords

Examples

			[0]        1
[1]       -1,      -1
[2]       -2,      -1,       0
[3]       -5,      -1,       1,      1
[4]       21,      25,      19,      9,       1
[5]     1103,     674,     343,    128,      23,      -2
[6]    29835,   15211,    6551,   2133,     379,     -25,     -9
[7]   739751,  331827,  123821,  33479,    3603,   -1549,   -583,    -9
[8] 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50

Crossrefs

Cf. A350256, A350257, A350258, A350259, A350260, A350261, A350263.
Cf. A000587, A009235.

Programs

  • Maple
    B := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
A350262 := (n, k) -> B(n, n - k + 1):
seq(seq(A350262(n, k), k = 0..n), n = 0..8);
  • Mathematica
    B[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]]; T[n_, k_] := B[n, n - k + 1];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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