A365122 - OEIS

%I #7 Aug 22 2023 13:18:50

%S 1,3,12,64,372,2319,15105,101649,701073,4929657,35207220,254690517,

%T 1862325262,13742311074,102204992352,765328009950,5765316776550,

%U 43661497944861,332217854059362,2538540859615095,19471592691620310,149871698475060433,1157188723053901449

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

%F If g.f. satisfies A(x) = (1 + x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*(n-k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

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

%Y Cf. A006013, A365113.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 22 2023