A379866 - OEIS

%I #13 Jan 05 2025 09:58:49

%S 1,0,2,-2,56,-222,5332,-45782,1127408,-15972542,428055644,-8598013734,

%T 256717806952,-6667767637598,223389539254676,-7076616268104278,

%U 265762684840216544,-9880557234248622462,413902270494309471436,-17591536945041528005318,816621849842712202724696

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379868.

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

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

%Y Cf. A108919, A367868.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jan 04 2025