A235685 E.g.f.: exp( Sum_{n>=1} H(n) * x^(2*n)/(2*n) ) where H(n) is the n-th harmonic number.

1, 1, 12, 370, 21490, 2012346, 276603096, 52410015372, 13086020092860, 4162089324641820, 1642246641208135248, 786999935144858519448, 450157417640763926225496, 302899153448396612425831800, 236824761815538353605549389600, 212892105513043495761147435785040

Offset: 0

Author

Paul D. Hanna, Jan 13 2014

Keywords

• nonn

Comments

Compare to: exp( Sum_{n>=1} x^(2*n)/(2*n) ) = 1/sqrt(1-x^2).

Examples

			E.g.f.: A(x) = 1 + x^2/2! + 12*x^4/4! + 370*x^6/6! + 21490*x^8/8! +...
where
log(A(x)) = x^2/2 + (1+1/2)*x^4/4 + (1+1/2+1/3)*x^6/6 + (1+1/2+1/3+1/4)*x^8/8 + (1+1/2+1/3+1/4+1/5)*x^10/10 + (1+1/2+1/3+1/4+1/5+1/6)*x^12/12 +...
Explicitly,
log(A(x)) = x^2/2! + 9*x^4/4! + 220*x^6/6! + 10500*x^8/8! + 828576*x^10/10! + 97796160*x^12/12! + 16145775360*x^14/14! + 3554072121600*x^16/16! +...
		

Crossrefs

Cf. A235385.

Programs

PARI

{H(n)=sum(k=1, n, 1/k)}
{a(n)=local(A=1); A=exp(sum(k=1, n\2+1, H(k)*x^(2*k)/(2*k))+x*O(x^n)); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(2*n), ", "))