This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009563 #33 Apr 16 2025 09:01:54
%S A009563 1,-4,56,-1688,84160,-6141312,613282944,-80158806016,13267800137728,
%T A009563 -2710082835353600,669033814167273472,-196220826200422416384,
%U A009563 67398310755666413387776,-26784943833122921085534208,12188704989839014070713057280,-6294241591527906725538628370432
%N A009563 Expansion of e.g.f. sin(x/cosh(x)) (odd powers only).
%H A009563 G. C. Greubel, <a href="/A009563/b009563.txt">Table of n, a(n) for n = 0..238</a>
%F A009563 a(n) = (-1)^n + 2*Sum_{m=0..n-1} binomial(2*n+1,2*m+1)*Sum_{j=0..(n-m)} binomial(m+j-1/2,j)*4^(n-m-j)*Sum_{i=0..j} (i-j)^(2*n-2*m)*binomial(2*j,i)*(-1)^(m+j-i). - _Vladimir Kruchinin_, Jun 16 2011
%t A009563 With[{nn=30},Take[CoefficientList[Series[Sin[x/Cosh[x]],{x,0,nn}],x] Range[ 0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Dec 24 2017 *)
%o A009563 (Maxima) a(n):=2*sum(binomial(2*n+1,2*m+1)*(sum(binomial(m+j-1/2,j)*4^(n-m-j)*sum((i-j)^(2*n-2*m)*binomial(2*j,i)*(-1)^(m+j-i),i,0,j),j,0,(n-m))),m,0,n-1)+(-1)^n; /* _Vladimir Kruchinin_, Jun 16 2011 */
%o A009563 (PARI) my(x='x+O('x^50)); v=Vec(serlaplace(sin(x/cosh(x)))); vector((#v-1)\2 ,n,v[2*n-1]) \\ _G. C. Greubel_, Jan 21 2018
%K A009563 sign
%O A009563 0,2
%A A009563 _R. H. Hardin_
%E A009563 Extended with signs by _Olivier Gérard_, Mar 15 1997