A249737 E.g.f.: Product_{k=1..n} cosh(k*x).

1, 0, 5, 0, 1992, 0, 6167551, 0, 73432708224, 0, 2389444075877425, 0, 173496878823412858880, 0, 24573448663070711791073155, 0, 6168942712247503719875933929472, 0, 2554865971518520622455831203134760669, 0, 1650933998542152349112398040415912949710848, 0

Offset: 0

Author

Vaclav Kotesovec, Nov 04 2014

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..235

Crossrefs

Cf. A249698, A177385, A177387, A001044 (e.g.f.: product_{k=1..n} sinh(k*x)).

Programs

Mathematica

Table[n!*SeriesCoefficient[Product[Cosh[k*x],{k,1,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[k!*Coefficient[tab[[k]],x^k],{k,1,nn}]}] (* more efficient *)

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 = 1.004120096780056350248342856...