A370196 - OEIS

%I #8 Feb 11 2024 09:15:52

%S 1,2,6,23,102,477,2259,10733,51174,245156,1180381,5709387,27723315,

%T 135055845,659744973,3230479173,15850993126,77918426928,383646423564,

%U 1891715752242,9340099603677,46170434726054,228479085858447,1131770152854441,5611302030239667

%N Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^3) )^n.

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*n,n-3*k).

%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)^2 * (1+x^3)) ). See A369443.

%o (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));

%Y Cf. A369443.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Feb 11 2024