A207137 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k*(n-k))*x^k ).

1, 1, 2, 4, 17, 171, 3171, 101741, 7181615, 1274607729, 428568152553, 223160743256395, 185627109707405932, 320952534083059792786, 1367454166673309618606950, 11078799748881429582280609036, 137939599816546528357634500253053, 2679390013936303204526656964298150849

Offset

0,3

Comments

The logarithmic derivative yields A207138.

Equals the antidiagonal sums of triangle A228900.

Links

Table of n, a(n) for n=0..17.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 17*x^4 + 171*x^5 + 3171*x^6 +...
where the logarithm of the g.f. equals the l.g.f. of A207138:
log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 51*x^4/4 + 761*x^5/5 + 17913*x^6/6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, x^m/m*sum(k=0, m, binomial(m^2, k*(m-k))*x^k))+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A207138 (log), A207135, A228900, A206850, A206830, A167006.

Sequence in context: A247260 A048872 A063800 * A355464 A143674 A136147

Adjacent sequences: A207134 A207135 A207136 * A207138 A207139 A207140

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2012

Status

approved