A121678 a(n) = [x^n] (1 + x*(1+x)^n )^(n+1).

1, 2, 9, 52, 425, 4236, 49294, 655096, 9731313, 159114880, 2832245911, 54400757016, 1119436524947, 24532373640334, 569732648555295, 13962373137304496, 359767723241891425, 9715902692094061488

Offset

0,2

Comments

a(n) is divisible by (n+1): a(n)/(n+1) = A121679(n).

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n+1} C(n+1,k) * C(n*k,n-k).

Example

At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6 = 4236, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...

Prog

(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial(n*k, n-k))

Crossrefs

Cf. A121679; variants: A121673-A121676, A121680.

Sequence in context: A369090 A110322 A161631 * A124347 A360743 A360193

Adjacent sequences: A121675 A121676 A121677 * A121679 A121680 A121681

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved