A167006 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) ).

1, 2, 6, 66, 4258, 1337374, 1933082159, 11353941470188, 291885138650054688, 29463501750534915665304, 12844314786465829040693498639, 21675661852919288704454219459892060, 156969579902607123047763327413679853875703

Offset

0,2

Comments

Logarithmic derivative yields A167009.

Equals row sums of triangle A209196.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..57

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 66*x^3 + 4258*x^4 + 1337374*x^5 +...
log(A(x)) = 2*x + 8*x^2/2 + 170*x^3/3 + 16512*x^4/4 + 6643782*x^5/5 + 11582386286*x^6/6 +...+ A167009(n)*x^n/n +...

Prog

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

Crossrefs

Cf. A167009, A209196, A155200.

Cf. variants: A206848, A228809.

Sequence in context: A217630 A091458 A335934 * A087331 A097419 A219037

Adjacent sequences: A167003 A167004 A167005 * A167007 A167008 A167009

Keyword

nonn

Author

Paul D. Hanna, Nov 17 2009

Status

approved