A372200 - OEIS

%I #7 Apr 22 2024 07:20:02

%S 1,2,12,116,1600,28832,643864,17190392,534707296,19003345568,

%T 760054943464,33798503960168,1654577248619728,88437537019736816,

%U 5125378381513865752,320163561707158120568,21445740148760729672896,1533498858453023915309888

%N E.g.f. A(x) satisfies A(x) = exp( 2 * x / (1 - x * A(x)^(1/2))^2 ).

%F E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A161635.

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

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

%Y Cf. A161630, A372201.

%Y Cf. A161635, A372160.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 21 2024