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A009269 Expansion of e.g.f. exp(tanh(x)*log(1+x)). 1
1, 0, 2, -3, 12, -70, 370, -2436, 20048, -175176, 1679368, -18271000, 216489416, -2751576048, 37874200208, -560956931640, 8845252164864, -148215651070272, 2635014886145472, -49474969983055872, 977864639612813440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = Sum_{m=1..n} Sum_{i=0..n-2*m} Stirling1(i+m,m)*binomial(n,i+m)* Sum_{k=0..n-i-2*m} binomial(k+m-1,m-1)*(k+m)!*(-1)^(2*m+k)*2^(n-k-i-2*m)*Stirling2(n-i-m,k+m), n > 0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

a(n) ~ n! * (-1)^n * n^(tanh(1)-1) / GAMMA(tanh(1)). - Vaclav Kotesovec, Jan 24 2015

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[Tanh[x]Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 19 2014 *)

CoefficientList[Series[(1 + x)^Tanh[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

PROG

(Maxima)

a(n):=sum(sum((stirling1(i+m, m)*binomial(n, i+m)*sum(binomial(k+m-1, m-1)*(k+m)!*(-1)^(2*m+k)*2^(n-k-i-2*m)*stirling2(n-i-m, k+m), k, 0, n-i-2*m)), i, 0, n-2*m), m, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */

CROSSREFS

Sequence in context: A012911 A264726 A099805 * A012396 A013012 A009594

Adjacent sequences:  A009266 A009267 A009268 * A009270 A009271 A009272

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Jan 19 2014

STATUS

approved

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Last modified July 30 09:18 EDT 2021. Contains 346359 sequences. (Running on oeis4.)