A121676 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1).

1, 2, 6, 32, 250, 2412, 27524, 360600, 5296050, 85805420, 1515794467, 28926900312, 591903009295, 12907255696636, 298428274844730, 7284351640977920, 187013495992710210, 5033669346061547724, 141643700005223732471

Offset

0,2

Comments

a(n) is divisible by (n+1): a(n)/(n+1) = A121677(n).

Links

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

Formula

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

Example

At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...

Prog

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

Crossrefs

Cf. A121677; variants: A121673-A121675, A121678-A121680.

Sequence in context: A211195 A346452 A012324 * A326096 A346270 A133596

Adjacent sequences: A121673 A121674 A121675 * A121677 A121678 A121679

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved