A177386 O.g.f.: Sum_{n>=0} Product_{k=1..n} sinh(k*arcsinh(2x)).

1, 2, 8, 48, 400, 4192, 52720, 773536, 12970016, 244625088, 5125896112, 118137655840, 2970016739552, 80883641686848, 2372035401856352, 74528583049288768, 2497667361588205632, 88932255196677684608

Offset: 0

Author

Paul D. Hanna, May 15 2010

Keywords

• nonn

Comments

Lim_{n->infinity} n!*A177386(n) / (2^n*A177385(n)) = 1. - Vaclav Kotesovec, Nov 06 2014

Examples

			O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 400*x^4 + 4192*x^5 + ...
Let G(x) be the e.g.f. of A177385:
G(x) = 1 + x + 4*x^2/2! + 37*x^3/3! + 616*x^4/4! + 16081*x^5/5! + ...
then A(x) = G(arcsinh(2x)).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A177385, A249748.

Programs

PARI

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

Formula

O.g.f.: A(x) = G(arcsinh(2x)) where G(x) = e.g.f. of A177385.

a(n) ~ c * d^n * n!, where d = 2*A249748 = 2.0937983852519084822268503..., c = 0.880333778211172907563073... (constant c is same as for A177385). - Vaclav Kotesovec, Nov 06 2014