A207135 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k*(n-k)) ).

1, 2, 5, 32, 796, 77508, 26058970, 28765221688, 101824384364586, 1145306676113095172, 40618070255705049577152, 4523562146025746408072408406, 1576501611479138389748204925102907, 1714649258669533421310212170714443813118

Offset

0,2

Comments

The logarithmic derivative yields A207136.

Equals the row sums of triangle A228900.

Equals the self-convolution of A228852.

Links

Table of n, a(n) for n=0..13.

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 32*x^3 + 796*x^4 + 77508*x^5 +...
where the logarithm of the g.f. equals the l.g.f. of A207136:
log(A(x)) = 2*x + 6*x^2/2 + 74*x^3/3 + 2942*x^4/4 + 379502*x^5/5 +...

Prog

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

Crossrefs

Cf. A207136 (log), A167006, A228900, A206830, A206850, A228852.

Sequence in context: A067299 A353195 A203227 * A118325 A224231 A357944

Adjacent sequences: A207132 A207133 A207134 * A207136 A207137 A207138

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2012

Status

approved