A121680 - OEIS

A121680

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

1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988

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OFFSET

0,2

COMMENTS

a(n) is divisible by (n+1): a(n)/(n+1) = A121681(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+1)*k,n-k).

EXAMPLE

At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^5 = 655, since

(1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*x^4 +...

MATHEMATICA

Table[Sum[Binomial[n+1, k] * Binomial[(n+1)*k, n-k], {k, 0, n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 02 2020 *)

PROG

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

CROSSREFS

Cf. A121681; variants: A121673-A121679.

Sequence in context: A037620 A198474 A285489 * A277478 A372410 A372233

Adjacent sequences: A121677 A121678 A121679 * A121681 A121682 A121683

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 15 2006

STATUS

approved