A365119 - OEIS

%I #7 Aug 22 2023 14:15:02

%S 1,3,6,19,69,267,1093,4629,20142,89473,404076,1849746,8563558,

%T 40025574,188612388,895115942,4274453904,20523807009,99025615998,

%U 479874362583,2334582421497,11398055887003,55828060595832,274254002718255,1350907899813921,6670789629569022

%N G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^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=1, 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. A001006, A365118.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 22 2023