A380800 - OEIS

%I #12 Feb 04 2025 08:59:42

%S 1,8,142,4088,165576,8711752,566093104,43882188408,3957135262720,

%T 407285038758536,47138933615042304,6062383519783848952,

%U 857919091977394542592,132511278843714141837000,22185703881021997753194496,4002648943012304165391154808,774212130931445685605345918976

%N Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-x / (1 - x)^2) * (1 - x)^3 ) )^2.

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) / (1 - x*A(x)^(1/2))^2 ) / (1 - x*A(x)^(1/2))^6.

%F a(n) = 2 * n! * Sum_{k=0..n} (n+2)^(k-1) * binomial(4*n+k+5,n-k)/k!.

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

%Y Cf. A380799, A380801.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 04 2025