A370098 - OEIS

%I #8 Feb 10 2024 09:23:27

%S 1,6,72,978,14016,207006,3116952,47568618,733189632,11387193846,

%T 177923724072,2793666465090,44042615547456,696708049377294,

%U 11053262513080440,175800225426741978,2802193910116429824,44752001810800994022,715924864099841086728

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

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

%F 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.

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

%Y Cf. A091527, A370097.

%Y Cf. A370099, A370102.

%Y Cf. A365843.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 10 2024