A207139 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k) * binomial(n^2,k^2) ).

1, 2, 7, 147, 14481, 6183605, 19196862399, 206667738393577, 6727813723143519624, 1368162090055314881480420, 1237384559488983889303951699285, 3014186760620644058660289396656407831, 34123084437870355957570087446546456971276065

Offset: 0

Author

Paul D. Hanna, Feb 15 2012

Keywords

• nonn

Comments

The logarithmic derivative yields A207140.

Examples

			G.f.: A(x) = 1 + 2*x + 7*x^2 + 147*x^3 + 14481*x^4 + 6183605*x^5 +...
where the logarithm of the g.f. equals the l.g.f. of A207140:
log(A(x)) = x + 2*x^2/2 + 10*x^3/3 + 407*x^4/4 + 56746*x^5/5 +...
		

Crossrefs

Cf. A207140 (log), A206850, A207135, A207137, A167006.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n+1,x^m/m*sum(k=0,m,binomial(m,k)*binomial(m^2,k^2))+x*O(x^n))),n)}
for(n=0,16,print1(a(n),", "))