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%I #20 Jan 17 2024 09:06:18
%S 0,0,2,-3,12,-40,190,-1071,7224,-56232,495898,-4880755,53005700,
%T -629398848,8110146070,-112690225935,1679413757168,-26719024870576,
%U 451969255722162,-8099650628337987,153288815339260796
%N Expansion of e.g.f. log(1+x)*sinh(x).
%D L. Comtet and M. Fiolet, Sur les dérivées successives d'une fonction implicite. C. R. Acad. Sci. Paris Ser. A 278 (1974), 249-251.
%F a(n) = n*((-1)^n*3F1(1,1,1-n;2;-1)+3F1(1,1,1-n;2;1))/2, n>0. - _Benedict W. J. Irwin_, May 30 2016
%F a(n) ~ (-1)^n * (n-1)! * sinh(1). - _Vaclav Kotesovec_, May 30 2016
%e log(1+x) * sinh(x) = x^2 -x^3/2 +x^4/2 -x^5/3 +19*x^6/72 -17*x^7/80 +...
%p A177699 := proc(n)
%p log(1+x)*sinh(x) ;
%p coeftayl(%,x=0,n)*n! ;
%p end proc;
%p seq(A177699(n),n=0..20) ; # _R. J. Mathar_, Nov 07 2011
%t Table[n ((-1)^n HypergeometricPFQ[{1, 1, 1 - n}, {2}, -1] + HypergeometricPFQ[{1, 1, 1 - n}, {2}, 1])/2, {n, 1, 20}] (* _Benedict W. J. Irwin_, May 30 2016 *)
%K sign
%O 0,3
%A _Michel Lagneau_, May 11 2010
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