A365113 - OEIS

%I #9 Aug 22 2023 07:57:31

%S 1,1,3,9,31,114,438,1739,7077,29364,123756,528324,2279868,9928679,

%T 43580301,192601419,856317717,3827501985,17188943523,77521747638,

%U 350959738842,1594390493067,7266093316649,33209221327752,152182572790008,699083290518817,3218624408121555

%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, then a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

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

%Y Cf. A000108, A365114, A365115.

%Y Cf. A161797, A365110.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 22 2023