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%I #26 Jan 27 2018 06:31:55
%S 1,0,2,-3,12,-70,370,-2436,20048,-175176,1679368,-18271000,216489416,
%T -2751576048,37874200208,-560956931640,8845252164864,-148215651070272,
%U 2635014886145472,-49474969983055872,977864639612813440
%N Expansion of e.g.f. exp(tanh(x)*log(1+x)).
%H Vincenzo Librandi, <a href="/A009269/b009269.txt">Table of n, a(n) for n = 0..200</a>
%F 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
%F a(n) ~ n! * (-1)^n * n^(tanh(1)-1) / GAMMA(tanh(1)). - _Vaclav Kotesovec_, Jan 24 2015
%t With[{nn=20},CoefficientList[Series[Exp[Tanh[x]Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 19 2014 *)
%t CoefficientList[Series[(1 + x)^Tanh[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)
%o (Maxima)
%o 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 */
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Previous Mathematica program replaced by _Harvey P. Dale_, Jan 19 2014
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