A370245 - OEIS

%I #9 Feb 13 2024 07:39:54

%S 1,2,16,110,828,6352,49696,393668,3148316,25362992,205519616,

%T 1673272702,13677016932,112165564656,922490228032,7605558361960,

%U 62839438825244,520180768020464,4313251202569216,35818392770702104,297846498752214128,2479748570715505472

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

%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(3*n-2*k-1,n-2*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^2)^3 ). See A369263.

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

%Y Cf. A288470, A360242.

%Y Cf. A369263.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024