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A317279 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*n^k*n!/k!. 3
1, 1, 0, -9, -32, 225, 3456, 2695, -433152, -4495743, 47872000, 1768142871, 6703534080, -597265448351, -11959736205312, 126058380654375, 9454322092343296, 84694164336894465, -5776865438988238848, -192541299662555831753, 1511905067561779200000, 243338391925401706938081, 3972949090873574466519040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the n-th term of the inverse Lah transform of the powers of n.

LINKS

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Transforms

FORMULA

a(n) = n! * [x^n] exp(n*x/(1 + x)).

a(n) = n! * [x^n] Product_{k>=1} exp(-n*(-x)^k).

MATHEMATICA

Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n - 1, k - 1] n^k n!/k!, {k, n}], {n, 22}]]

Table[n! SeriesCoefficient[Exp[n x/(1 + x)], {x, 0, n}], {n, 0, 22}]

Table[n! SeriesCoefficient[Product[Exp[-n (-x)^k], {k, 1, n}], {x, 0, n}], {n, 0, 22}]

Join[{1}, Table[(-1)^(n + 1) n n! Hypergeometric1F1[1 - n, 2, n], {n, 22}]]

CROSSREFS

Cf. A111884, A293145, A317277, A317278.

Sequence in context: A297298 A229444 A300773 * A196016 A183426 A061913

Adjacent sequences:  A317276 A317277 A317278 * A317280 A317281 A317282

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 25 2018

STATUS

approved

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Last modified August 14 13:51 EDT 2020. Contains 336481 sequences. (Running on oeis4.)