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

Author

Paul D. Hanna, Nov 17 2009

Keywords

• nonn

Comments

Logarithmic derivative yields A167009.

Equals row sums of triangle A209196.

Examples

			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 +...
		

Links

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

Crossrefs

Cf. A167009, A209196, A155200.

Cf. variants: A206848, A228809.

Programs

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),", "))