A228809 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) ).

1, 2, 4, 12, 94, 2195, 158904, 31681195, 13904396167, 15305894726347, 44888344014554903, 288228807835914177564, 4270880356112396772814732, 169380654509201278629725097906, 15394658527137259981745081997280638, 3042352591056504014301304188228238554499

Offset

0,2

Comments

Logarithmic derivative equals A228808.

Equals row sums of triangle A228904.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..73

Example

G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 94*x^4 + 2195*x^5 +...
where
log(A(x)) = 2*x + 4*x^2/2 + 20*x^3/3 + 296*x^4/4 + 10067*x^5/5 + 927100*x^6/6 +...+ A228808(n)*x^n/n +...

Prog

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

Crossrefs

Cf. A228808, A207135, A228904.

Cf. variants: A167006, A206848.

Sequence in context: A217041 A120618 A259048 * A326945 A309718 A230814

Adjacent sequences: A228806 A228807 A228808 * A228810 A228811 A228812

Keyword

nonn

Author

Paul D. Hanna, Sep 04 2013

Status

approved