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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.

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

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OFFSET

0,13

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

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

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

CROSSREFS

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

Cf. A000587, A318183.

Sequence in context: A357184 A228610 A106677 * A091592 A174372 A145906

Adjacent sequences: A350258 A350259 A350260 * A350262 A350263 A350264

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Dec 22 2021

STATUS

approved