A373741 - OEIS

%I #8 Jun 16 2024 11:02:07

%S 1,0,1,9,39,150,1365,13545,105945,918540,10603845,127806525,

%T 1468823895,18253765530,257397445305,3770163121725,55637459903025,

%U 866703333295800,14468243658093225,250223925107581425,4426399346291497575,81488489549760042750

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

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

%F a(n) = (n-1)/2 * (2*a(n-2) + 9*(n-2)*a(n-3) + 12*(n-2)*(n-3)*a(n-4) + 5*(n-2)*(n-3)*(n-4)*a(n-5)).

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

%Y Cf. A361567, A373740.

%Y Cf. A116090.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 16 2024