A378151 - OEIS

%I #10 Nov 18 2024 07:33:10

%S 1,0,0,1,3,3,4,18,45,72,153,450,1066,2172,5142,13381,31752,72333,

%T 176475,441909,1065528,2551465,6292857,15620439,38229235,93698523,

%U 232545105,578019090,1430290512,3548336724,8851036863,22092054588,55093739760,137681640450

%N G.f. A(x) satisfies A(x) = 1 + (x * (1+x) * A(x))^3.

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

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

%Y Cf. A000045, A256169, A378152.

%Y Cf. A115055, A378153.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Nov 18 2024