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A249698
E.g.f.: Sum_{n>=0} Product_{k=1..n} cosh(k*x).
3
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
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