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A009199 Expansion of e.g.f. exp(log(1+x)^2). 7
1, 0, 2, -6, 34, -220, 1688, -14868, 147684, -1631376, 19821912, -262573080, 3764276712, -58044604176, 957653604672, -16828739439120, 313742795670288, -6183918938706048, 128463999017594016, -2804979941504113248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..446

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 128

FORMULA

a(n) = Sum_{k=0..floor(n/2)} Stirling1(n, 2*k)*(2*k)!/k!. - Vladeta Jovovic, Sep 21 2003

E.g.f.: (1+x)^(log(1+x)). - Vaclav Kotesovec, Jul 31 2018

a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,2) * a(n-k). - Seiichi Manyama, May 06 2022

MATHEMATICA

CoefficientList[Series[E^(Log[1+x]^2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 02 2015 *)

PROG

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, binomial(i-1, j-1)*stirling(j, 2, 1)*v[i-j+1])); v; \\ Seiichi Manyama, May 06 2022

CROSSREFS

Sequence in context: A253778 A346189 A018953 * A052824 A019029 A019032

Adjacent sequences:  A009196 A009197 A009198 * A009200 A009201 A009202

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

STATUS

approved

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Last modified August 11 11:29 EDT 2022. Contains 356065 sequences. (Running on oeis4.)