A182529 E.g.f.: exp( Sum_{n>=1} x^n * Sum_{k=1..n} 1/k^2 ) = Sum_{n>=0} a(n)*x^n/n!^2.

1, 1, 7, 100, 2438, 90246, 4702142, 327233880, 29271020760, 3268118467608, 445031112068232, 72541135526581536, 13936782476047959024, 3115165518696599108976, 801181037747755210248432, 234835083029394312036638016, 77797056535321496989078410624

Offset: 0

Author

Paul D. Hanna, May 03 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 7*x^2/2!^2 + 100*x^3/3!^2 + 2438*x^4/4!^2 + 90246*x^5/5!^2 +...
such that
log(A(x)) = x + x^2*(1+1/4) + x^3*(1+1/4+1/9) + x^4*(1+1/4+1/9+1/16) + x^5*(1+1/4+1/9+1/16+1/25) + x^6*(1+1/4+1/9+1/16+1/25+1/36) +...
		

Crossrefs

Cf. A087761.

Programs

PARI

{a(n)=n!^2*polcoeff(exp(sum(m=1, n+1, x^m*sum(k=1, m, 1/k^2)+x*O(x^n))), n)}
for(n=0,20,print1(a(n),", "))