A351941 a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k) * a(n-2*k-1).

1, -1, 1, 0, -3, 8, -3, -57, 225, -96, -2991, 13873, -255, -313506, 1495089, 1473024, -54621231, 243365688, 705129201, -14109279483, 53228648865, 349791931434, -5000315242479, 13572033641204, 204954070915977, -2294997521498172, 2691551249257017

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

• sign

Crossrefs

Cf. A101912, A138314.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n - 1, 2 k] a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 26}]

Formula

E.g.f.: exp( -Sum_{n>=0} a(n) * x^(2*n+1) / (2*n+1)! ).