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

0,2

Comments

The logarithmic derivative yields A207140.

Links

Table of n, a(n) for n=0..12.

Example

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 +...

Prog

(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), ", "))

Crossrefs

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

Sequence in context: A101799 A201172 A062617 * A064607 A182974 A005345

Adjacent sequences: A207136 A207137 A207138 * A207140 A207141 A207142

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2012

Status

approved