A121674 a(n) = [x^n] (1 + x*(1+x)^n )^n.

1, 1, 5, 28, 233, 2376, 28102, 379016, 5707025, 94439440, 1699067321, 32951077193, 684009742319, 15110032165151, 353485501643471, 8721374385748256, 226128389777924385, 6142306518887606112, 174311816444805024379

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

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

Example

At n=4, a(4) = [x^4] (1 + x*(1+x)^4 )^4 = 233, since
(1 + x*(1+x)^4 )^4 = 1 + 4*x + 22*x^2 + 76*x^3 + 233*x^4 +...

Mathematica

Table[Sum[Binomial[n, k] * Binomial[n*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 12 2015 *)

Prog

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

Crossrefs

Cf. variants: A121673, A121675-A121680.

Sequence in context: A038172 A183375 A000530 * A306181 A362690 A116977

Adjacent sequences: A121671 A121672 A121673 * A121675 A121676 A121677

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved