A225604 G.f.: exp( Sum_{n>=1} A002426(n^2) * x^n/n ), where A002426 is the central trinomial coefficients.

1, 1, 10, 1056, 1300253, 16436676927, 2026538428535847, 2377041996570919354629, 26137381916593225072659360863, 2668615348740645885804068311893052895, 2513426521807431879643802805359800329740903335, 21735453667359385540995804455408000917620356989063370267

Offset: 0

Author

Paul D. Hanna, Aug 03 2013

Keywords

• nonn

Examples

			G.f.: A(x) = A(x) = 1 + x + 10*x^2 + 1056*x^3 + 1300253*x^4 + 16436676927*x^5 +...
where
log(A(x)) = x + 19*x^2/2 + 3139*x^3/3 + 5196627*x^4/4 + 82176836301*x^5/5 +...+ A225602(n)*x^n/n +...
		

Crossrefs

Cf. A225602, A002426.

Programs

PARI

{A002426(n)=sum(k=0,n, binomial(n, k)*binomial(k, n-k))}
{a(n)=polcoeff(exp(sum(m=1,n+1,A002426(m^2)*x^m/m) +x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A225602.