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A334241 a(n) = exp(n) * Sum_{k>=0} (k + 1)^n * (-n)^k / k!. 5
1, 0, -1, 7, -43, 221, -341, -15980, 370761, -5688125, 62689871, -197586839, -14973562979, 585250669316, -14306382821485, 240985102271971, -1121421968408303, -122020498882279931, 6674724196051810807, -223424819176020519168, 5051515662105879438501 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Bell Polynomial

FORMULA

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (-n*x/(1 - x))^k / Product_{j=1..k} (1 - j*x/(1 - x)).

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

a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(-n).

MATHEMATICA

Table[n! SeriesCoefficient[Exp[x + n (1 - Exp[x])], {x, 0, n}], {n, 0, 20}]

Table[Sum[Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A292866, A334193, A334240, A334242, A334243.

Sequence in context: A193697 A027176 A244200 * A079925 A126718 A081896

Adjacent sequences:  A334238 A334239 A334240 * A334242 A334243 A334244

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 19 2020

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)