OFFSET
0,3
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..250
FORMULA
a(n) ~ c * d^n * (n!)^2, where d = A249748 = 1.04689919262595424111342518325311817976789046475647184115584744582777576864..., c = 0.880333778211172907563073031129920597506533414605109200048966773434616066... . - Vaclav Kotesovec, Nov 04 2014
EXAMPLE
E.g.f: A(x) = 1 + x + 4*x^2/2! + 37*x^3/3! + 616*x^4/4! +...
A(x) = 1 + sinh(x) + sinh(x)*sinh(2x) + sinh(x)*sinh(2x)*sinh(3x) + ...
MATHEMATICA
Table[n!*SeriesCoefficient[Sum[Product[Sinh[k*x], {k, 1, j}], {j, 0, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 01 2014 *)
nn=20; tab = ConstantArray[0, nn]; tab[[1]] = Series[Sinh[x], {x, 0, nn}]; Do[tab[[k]] = Series[tab[[k-1]]*Sinh[k*x], {x, 0, nn}], {k, 2, nn}]; Flatten[{1, Rest[CoefficientList[Sum[tab[[k]], {k, 1, nn}], x] * Range[0, nn]!]}] (* Vaclav Kotesovec, Nov 04 2014 (more efficient) *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, sinh(k*X))); n!*polcoeff(Egf, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 15 2010
STATUS
approved