A196559 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k]^2 * x^n/n ).

1, 1, 3, 12, 65, 384, 2197, 14078, 94739, 670612, 4899280, 36645899, 281037158, 2197679518, 17489660228, 141241307806, 1155345218645, 9559672712389, 79905432682918, 674005489358155, 5731854529045978, 49105864505432392, 423531623342726441

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 65*x^4 + 384*x^5 + 2197*x^6 +...
where
log(A(x)) = (1 + x)^2*x + (1+2^3*x+x^2)^2*x^2/2 + (1+3^3*x+3^3*x^2+x^3)^2*x^3/3 + (1+4^3*x+6^3*x^2+4^3*x^3+x^4)^2*x^4/4 +...
More explicitly,
log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 205*x^4/4 + 1506*x^5/5 + 10016*x^6/6 +...

Prog

 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^3*x^k)^2*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A166896, A180718, A196560.

Sequence in context: A341769 A302195 A359660 * A111262 A139134 A216373

Adjacent sequences: A196556 A196557 A196558 * A196560 A196561 A196562

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2011

Status

approved