A210443 G.f.: Sum_{n>=0} x^n * (1 + n^2*x)^n / (1 + x + n^2*x^2)^n.

1, 1, 1, 6, 21, 150, 962, 8640, 80220, 884520, 10709520, 140873040, 2098741680, 32163828480, 568234774800, 9957054159360, 203333391011520, 4013297314266240, 92967912795139200, 2041979786688441600, 52890421861957680000, 1279950952105367942400, 36648398470742114918400

Offset

0,4

Comments

a(n) is divisible by ((n-1)/2)! for n>0.

Compare to the g.f. of A187741:

Sum_{n>=0} x^n*(1+n*x)^n/(1+x+n*x^2)^n = 1/2 + (1+2*x)*Sum_{n>=0} (n+1)!*x^(2*n)/2.

Links

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

Example

G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 21*x^4 + 150*x^5 + 962*x^6 + 8640*x^7 +...
where
A(x) = 1 + (1+x)*x/(1+x+x^2) + (1+4*x)^2*x^2/(1+x+4*x^2)^2 + (1+9*x)^3*x^3/(1+x+9*x^2)^3 + (1+16*x)^4*x^4/(1+x+16*x^2)^4 + (1+25*x)^5*x^5/(1+x+25*x^2)^5 +...

Prog

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

Crossrefs

Cf. A187741.

Sequence in context: A058821 A054366 A304264 * A179768 A131960 A244299

Adjacent sequences: A210440 A210441 A210442 * A210444 A210445 A210446

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2013

Status

approved