A215529 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..n} (1 + k*x)^3.

1, 1, 4, 31, 377, 6415, 142252, 3919208, 129681162, 5025119715, 223662035160, 11260717242863, 633424125262667, 39405127536106444, 2688050940578533440, 199621706483099855304, 16038639938585081005722, 1386688821351774846453155, 128409360760837836935472512

Offset

0,3

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x).

Links

Table of n, a(n) for n=0..18.

Example

G.f.: 1/(1-x) = 1 + 1*x/(1+x)^3 + 4*x^2/((1+x)*(1+2*x))^3 + 31*x^3/((1+x)*(1+2*x)*(1+3*x))^3 + 377*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^3 +...

Prog

(PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, k, 1+j*x+x*O(x^n))^3), n))}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A118804, A208829, A193333.

Sequence in context: A369737 A198865 A145087 * A351798 A005046 A323568

Adjacent sequences: A215526 A215527 A215528 * A215530 A215531 A215532

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2012

Status

approved