A177388 O.g.f.: Sum_{n>=0} Product_{k=1..n} sin(k*arcsin(2x)).

1, 2, 8, 48, 368, 3488, 39408, 517536, 7747552, 130224448, 2428303280, 49745334816, 1110519910176, 26832869319872, 697671946188128, 19422303020653632, 576390053072381888, 18164695560213480064

Offset: 0

Author

Paul D. Hanna, May 15 2010

Keywords

• nonn

Examples

			O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 368*x^4 + 3488*x^5 + ...
Let G(x) be the e.g.f. of A177387:
G(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 536*x^4/4! + ...
then A(x) = G(arcsin(2*x)).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..260

Crossrefs

Cf. A177387.

Programs

PARI

{a(n)=local(X=x+x*O(x^n),Ogf);Ogf=sum(m=0,n,prod(k=1,m,sin(k*asin(2*X))));polcoeff(Ogf,n)}

Formula

O.g.f.: A(x) = G(arcsin(2x)) where G(x) = e.g.f. of A177387.

a(n) ~ c * (4/(Pi*log(2)))^n * n! * n^(1/6), where c = 1.01529686... . - Vaclav Kotesovec, Nov 04 2014