A378730 - OEIS

%I #10 Dec 06 2024 11:10:27

%S 1,2,3,10,35,134,544,2288,9907,43830,197300,900738,4160521,19408084,

%T 91302317,432663728,2063421045,9896113574,47698770359,230932635206,

%U 1122545149941,5476405604806,26805046064328,131595640014314,647829955225386,3197267300375652

%N G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)^(3/2)) )^2.

%F G.f.: A(x) = (1 + x*B(x))^2 where B(x) is the g.f. of A364742.

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

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

%Y Cf. A364742, A365119.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 05 2024