cp's OEIS Frontend

A003717 Expansion of e.g.f. sin(tanh(x)) (odd powers only).

%I A003717 M3143 #28 Jan 28 2018 02:27:50
%S A003717 1,-3,37,-959,41641,-2693691,241586893,-28607094455,4315903789009,
%T A003717 -807258131578995,183184249105857781,-49548882107764546223,
%U A003717 15742588857552887269753,-5802682207845642276301995
%N A003717 Expansion of e.g.f. sin(tanh(x)) (odd powers only).
%D A003717 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003717 Vincenzo Librandi, <a href="/A003717/b003717.txt">Table of n, a(n) for n = 0..100</a>
%F A003717 a(n) = (-1)^(n-1)*b(2*n-1), b(n) = sum(k=1..n,(1-(-1)^k)/k!*((-1)^(n-k)+1)* sum(j=k..n, binomial(j-1,k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)* Stirling2(n,j))). - _Vladimir Kruchinin_, Apr 21 2011
%t A003717 Sin[ Tanh[ x ] ] (* Odd Part *)
%t A003717 With[{nn = 60}, Take[CoefficientList[Series[Sin[Tanh[x]], {x, 0, nn}], x] Range[0, nn - 1]!, {2, -1, 2}]] (* _Vincenzo Librandi_, Apr 11 2014 *)
%o A003717 (Maxima)
%o A003717 a(n):=(-1)^(n-1)*b(2*n-1);
%o A003717 b(n):=sum((1-(-1)^k)/k!*((-1)^(n-k)+1)*sum(binomial(j-1,k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)*stirling2(n,j),j,k,n),k,1,n); /* _Vladimir Kruchinin_, Apr 21 2011 */
%K A003717 sign
%O A003717 0,2
%A A003717 _R. H. Hardin_, _Simon Plouffe_
%E A003717 Name edited by _Michel Marcus_, Jan 28 2018