cp's OEIS Frontend

A249698 E.g.f.: Sum_{n>=0} Product_{k=1..n} cosh(k*x).

%I A249698 #11 Nov 04 2014 09:07:56
%S A249698 1,0,6,0,2426,0,7553776,0,90192976308,0,2939813898295990,0,
%T A249698 213701821328573755046,0,30292525174041077292043440,0,
%U A249698 7609302838629919155170452856136,0,3152886110080180503361685427596189430,0,2038143533263759863560759054752335955960482
%N A249698 E.g.f.: Sum_{n>=0} Product_{k=1..n} cosh(k*x).
%H A249698 Vaclav Kotesovec, <a href="/A249698/b249698.txt">Table of n, a(n) for n = 0..234</a>
%F A249698 If n is even a(n) ~ c * d^n * n^(2*n) / (2^(2*n-2) * exp(2*n)), where d = 8.9061971328050809899679389417314..., c = 1.243878632396819914960247452516...
%t A249698 Table[n!*SeriesCoefficient[Sum[Product[Cosh[k*x],{k,1,j}],{j,0,n}],{x,0,n}],{n,0,20}]
%t A249698 nn=20; tab = ConstantArray[0,nn]; tab[[1]] = Series[Cosh[x],{x,0,nn}]; Do[tab[[k]] = Series[tab[[k-1]]*Cosh[k*x],{x,0,nn}],{k,2,nn}]; Flatten[{1,Table[kk!*Sum[Coefficient[tab[[k]],x^kk],{k,1,kk}],{kk,1,nn}]}] (* more efficient *)
%o A249698 (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, cosh(k*X))); n!*polcoeff(Egf, n)}
%o A249698 for(n=0, 20, print1(a(n), ", "))
%Y A249698 Cf. A177385, A224899, A249489, A177387, A249737.
%K A249698 nonn
%O A249698 0,3
%A A249698 _Vaclav Kotesovec_, Nov 04 2014