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

0,3

Links

Table of n, a(n) for n=0..11.

Formula

Logarithmic derivative yields A225602.

Example

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 +...

Prog

(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), ", "))

Crossrefs

Cf. A225602, A002426.

Sequence in context: A103623 A145184 A004810 * A208560 A263311 A190945

Adjacent sequences: A225601 A225602 A225603 * A225605 A225606 A225607

Keyword

nonn,changed

Author

Paul D. Hanna, Aug 03 2013

Status

approved