A379861 - OEIS

%I #10 Jan 05 2025 09:58:41

%S 1,1,5,38,441,6714,128245,2943562,79049201,2432351618,84408126621,

%T 3261942050058,138946757581225,6468600047278498,326782092756236741,

%U 17805164917279808234,1040857709162817298401,64983981546315031200258,4315627103007355018430509

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

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

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

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

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

%Y Cf. A377553, A379862.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 04 2025