A391406 - OEIS

%I #9 Dec 09 2025 08:17:15

%S 1,3,14,68,352,1895,10509,59619,344380,2018599,11976479,71786394,

%T 434049233,2644251959,16214959902,100008206636,619980261922,

%U 3861037683008,24144159455460,151540706064143,954348342189353,6028591984661431,38189462008586184,242544213458754883

%N Expansion of g^4/(1 + x*g), where g = 1+x*g^3 is the g.f. of A001764.

%F a(n) = Sum_{k=0..n} (-1)^k * (k+4) * binomial(3*n-2*k+4,n-k)/(3*n-2*k+4).

%o (PARI) a(n) = sum(k=0, n, (-1)^k*(k+4)*binomial(3*n-2*k+4, n-k)/(3*n-2*k+4));

%Y Cf. A023053, A391294, A391404.

%Y Cf. A001558, A001764.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 08 2025