A158265 G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n+1)*x^n/n ).

1, 2, 11, 74, 697, 8002, 115158, 1949640, 38662510, 872245634, 22150393253, 623661939852, 19296665400632, 650198159192554, 23700604926216759, 928939297013294294, 38956230043045053042, 1740248411222193973416

Offset: 0

Author

Paul D. Hanna, Mar 29 2009

Keywords

• nonn

Comments

Definition: sigma(n,n+1) = Sum_{d|n} d^(n+1): [1,9,82,1057,15626,...].

Examples

			G.f.: A(x) = 1 + 2*x + 11*x^2 + 74*x^3 + 697*x^4 + 8002*x^5 +...
log(A(x)) = 2*x + 18*x^2/2 + 164*x^3/3 + 2114*x^4/4 + 31252*x^5/5 +...
		

Crossrefs

Cf. A158095, A023881, A082245.

Programs

PARI

a(n)=polcoeff(exp(sum(m=1, n, 2*sigma(m, m+1)*x^m/m)+x*O(x^n)), n)

Formula

a(n) ~ 2 * exp(1) * n^(n-1). - Vaclav Kotesovec, Oct 31 2024