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

0,3

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

Cf. A177385, A224899, A249489, A177387, A249737.

Sequence in context: A218343 A122192 A357801 * A284452 A357802 A109006

Adjacent sequences: A249695 A249696 A249697 * A249699 A249700 A249701

Keyword

nonn

Author

Vaclav Kotesovec, Nov 04 2014

Status

approved