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A331725 E.g.f.: exp(x/(1 - x)) / (1 + x). 0
1, 0, 3, 4, 57, 216, 2755, 18348, 247569, 2368432, 35256771, 436248660, 7235178313, 108919083144, 2010150360387, 35421547781116, 723689454172065, 14543895730321248, 326843345169621379, 7354350135365751972, 180610925178770615001, 4488323611011676811320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * k! * A000262(n-k).

a(n) ~ n^(n - 1/4) / (2^(3/2) * exp(1/2 - 2*sqrt(n) + n)). - Vaclav Kotesovec, Jan 26 2020

MATHEMATICA

nmax = 21; CoefficientList[Series[Exp[x/(1 - x)]/(1 + x), {x, 0, nmax}], x] Range[0, nmax]!

A000262[n_] := If[n == 0, 1, n! Sum[Binomial[n - 1, k]/(k + 1)!, {k, 0, n - 1}]]; a[n_] := Sum[(-1)^k Binomial[n, k] k! A000262[n - k], {k, 0, n}]; Table[a[n], {n, 0, 21}]

PROG

(PARI) seq(n)={Vec(serlaplace(exp(x/(1 - x) + O(x*x^n)) / (1 + x)))} \\ Andrew Howroyd, Jan 25 2020

CROSSREFS

Cf. A000262, A002720, A009940, A133942, A182386.

Sequence in context: A132678 A166850 A317856 * A067093 A041105 A196442

Adjacent sequences:  A331722 A331723 A331724 * A331726 A331727 A331728

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 25 2020

STATUS

approved

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Last modified May 10 22:15 EDT 2021. Contains 343780 sequences. (Running on oeis4.)