A249698 E.g.f.: Sum_{n>=0} Product_{k=1..n} cosh(k*x).
1, 0, 6, 0, 2426, 0, 7553776, 0, 90192976308, 0, 2939813898295990, 0, 213701821328573755046, 0, 30292525174041077292043440, 0, 7609302838629919155170452856136, 0, 3152886110080180503361685427596189430, 0, 2038143533263759863560759054752335955960482
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..234
Programs
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Mathematica
Table[n!*SeriesCoefficient[Sum[Product[Cosh[k*x],{k,1,j}],{j,0,n}],{x,0,n}],{n,0,20}] 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 *) -
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)} for(n=0, 20, print1(a(n), ", "))
Formula
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...