A379866 Expansion of e.g.f. (1/x) * Series_Reversion( x / (exp(-x) + x)^2 ).

1, 0, 2, -2, 56, -222, 5332, -45782, 1127408, -15972542, 428055644, -8598013734, 256717806952, -6667767637598, 223389539254676, -7076616268104278, 265762684840216544, -9880557234248622462, 413902270494309471436, -17591536945041528005318, 816621849842712202724696

Offset: 0

Author

Seiichi Manyama, Jan 04 2025

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A108919, A367868.

Programs

PARI

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

Formula

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

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

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