A370098 a(n) = Sum_{k=0..n} binomial(3*n,k) * binomial(4*n-k-1,n-k).

1, 6, 72, 978, 14016, 207006, 3116952, 47568618, 733189632, 11387193846, 177923724072, 2793666465090, 44042615547456, 696708049377294, 11053262513080440, 175800225426741978, 2802193910116429824, 44752001810800994022, 715924864099841086728

Offset

0,2

Links

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

Formula

a(n) = [x^n] ( (1+x)^3/(1-x)^3 )^n.

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^3 ). See A365843.

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n, k)*binomial(4*n-k-1, n-k));

Crossrefs

Cf. A091527, A370097.

Cf. A370099, A370102.

Cf. A365843.

Sequence in context: A113331 A333593 A214159 * A303342 A332705 A237021

Adjacent sequences: A370095 A370096 A370097 * A370099 A370100 A370101

Keyword

nonn

Author

Seiichi Manyama, Feb 10 2024

Status

approved