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A318183 a(n) = [x^n] Sum_{k>=0} x^k/Product_{j=1..k} (1 + n*j*x). 0
1, 1, -1, 1, 25, -674, 15211, -331827, 5987745, 15901597, -13125035449, 1292056076070, -103145930581319, 7462324963409941, -464957409070517453, 16313974895147212801, 2059903411953959582849, -708700955022151333496910, 143215213612865558214820303, -24681846509158429152517973103 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Bell Polynomial

FORMULA

a(n) = n! * [x^n] exp((1 - exp(-n*x))/n), for n > 0.

a(n) = Sum_{k=0..n} (-n)^(n-k)*Stirling2(n,k).

a(n) = (-n)^n*BellPolynomial_n(-1/n) for n >= 1. - Peter Luschny, Aug 20 2018

MATHEMATICA

Table[SeriesCoefficient[Sum[x^k/Product[(1 + n j x), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 19}]

Join[{1}, Table[n! SeriesCoefficient[Exp[(1 - Exp[-n x])/n], {x, 0, n}], {n, 19}]]

Join[{1}, Table[Sum[(-n)^(n - k) StirlingS2[n, k], {k, n}], {n, 19}]]

Join[{1}, Table[(-n)^n BellB[n, -1/n], {n, 1, 21}]] (* Peter Luschny, Aug 20 2018 *)

CROSSREFS

Cf. A009235, A014182, A292866, A301419, A317996, A318179, A318180, A318181.

Sequence in context: A153111 A097194 A180811 * A015697 A099365 A215017

Adjacent sequences:  A318180 A318181 A318182 * A318184 A318185 A318186

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Aug 20 2018

STATUS

approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)