A373720 - OEIS

%I #9 Jun 15 2024 09:23:19

%S 1,1,1,19,73,541,5761,35911,515089,5399353,61253281,991270171,

%T 11862564121,203249068309,3295367161633,52595413358671,

%U 1060046073787681,18422593177204081,383150483373313729,8042585703164409763,165930214242407069161,3968988522451484425741

%N Expansion of e.g.f. exp(x * (1 + x^2)^3).

%F a(n) = n! * Sum_{k=0..floor(3*n/7)} binomial(3*n-6*k,k)/(n-2*k)!.

%F a(n) == 1 (mod 18).

%F a(n) = a(n-1) + 9*(n-1)*(n-2)*a(n-3) + 15*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) + 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-7).

%o (PARI) a(n) = n!*sum(k=0, 3*n\7, binomial(3*n-6*k, k)/(n-2*k)!);

%Y Cf. A361279, A373718.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 15 2024