A221973 G.f.: Sum_{n>=0} n! * x^n * Product_{k=1..n} (3 + k*x)/(1 + 3*k*x + k^2*x^2).

1, 3, 10, 39, 183, 1026, 6695, 49623, 411050, 3763599, 37757055, 411894882, 4854301087, 61459583007, 831926801290, 11989221944871, 183273754945959, 2961997167865410, 50462267599637975, 903853088211536295, 16980055625062979306, 333846342195447641343

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Example

 G.f.: A(x) = 1 + 3*x + 10*x^2 + 39*x^3 + 183*x^4 + 1026*x^5 + 6695*x^6 +...
where
A(x) = 1 + x*(3+x)/(1+3*x+x^2) + 2!*x^2*(3+x)*(3+2*x)/((1+3*x+x^2)*(1+6*x+4*x^2)) + 3!*x^3*(3+x)*(3+2*x)*(3+3*x)/((1+3*x+x^2)*(1+6*x+4*x^2)*(1+9*x+9*x^2)) + 4!*x^4*(3+x)*(3+2*x)*(3+3*x)*(3+4*x)/((1+3*x+x^2)*(1+6*x+4*x^2)*(1+9*x+9*x^2)*(1+12*x+16*x^2)) +...

Prog

 (PARI) {a(n)=polcoeff( sum(m=0, n, m!*x^m*prod(k=1, m, (3+k*x)/(1+3*k*x+k^2*x^2 +x*O(x^n))) ), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A208237, A136127.

Sequence in context: A087860 A307593 A351144 * A303004 A054912 A093463

Adjacent sequences: A221970 A221971 A221972 * A221974 A221975 A221976

Keyword

nonn

Author

Paul D. Hanna, Feb 01 2013

Status

approved