OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..253
Vaclav Kotesovec, Graph of 1000 terms (limit to constant c)
FORMULA
a(n) ~ c * 2^(n+1) * n^(2*n+7/6) / (Pi^(n-1) * exp(2*n) * (log(2))^n), where c = 1.01529686... . - Vaclav Kotesovec, Nov 03 2014
EXAMPLE
E.g.f: A(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 536*x^4/4! +...
A(x) = 1 + sin(x) + sin(x)*sin(2x) + sin(x)*sin(2x)*sin(3x) + ...
MATHEMATICA
Flatten[{1, Rest[CoefficientList[Series[Sum[Product[Sin[m*x], {m, 1, k}], {k, 1, 20}], {x, 0, 20}], x] * Range[0, 20]!]}] (* Vaclav Kotesovec, Nov 03 2014 *)
nn=20; tab=ConstantArray[0, nn]; tab[[1]]=Series[Sin[x], {x, 0, nn}]; Do[tab[[k]]=Series[tab[[k-1]]*Sin[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 03 2014 (more efficient) *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, sin(k*X))); n!*polcoeff(Egf, n)}
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Paul D. Hanna, May 15 2010
STATUS
approved