A379688 - OEIS

%I #16 Jan 12 2025 10:17:28

%S 1,2,20,366,9992,365130,16769292,929022206,60323670416,4494465562770,

%T 378025706776340,35434198578761862,3663111561838580568,

%U 414057463231218044186,50805545997014472821276,6725525908390393438264590,955435863749903677193184032,144987884255349864723586105122

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

%H Seiichi Manyama, <a href="/A379688/b379688.txt">Table of n, a(n) for n = 0..326</a>

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

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380095.

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

%Y Cf. A213644, A380097.

%Y Cf. A379659, A379687.

%Y Cf. A380095.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 29 2024