OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..234
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...
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 *)
PROG
(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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 04 2014
STATUS
approved