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E.g.f.: Product_{k=1..n} cosh(k*x).
2

%I #8 Nov 04 2014 09:11:02

%S 1,0,5,0,1992,0,6167551,0,73432708224,0,2389444075877425,0,

%T 173496878823412858880,0,24573448663070711791073155,0,

%U 6168942712247503719875933929472,0,2554865971518520622455831203134760669,0,1650933998542152349112398040415912949710848,0

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

%H Vaclav Kotesovec, <a href="/A249737/b249737.txt">Table of n, a(n) for n = 0..235</a>

%F 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...

%t Table[n!*SeriesCoefficient[Product[Cosh[k*x],{k,1,n}],{x,0,n}],{n,0,20}]

%t 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 *)

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Nov 04 2014