A384757 E.g.f. A(x) satisfies A(x) = exp( -x * A(-x*A(x)) ).

1, -1, -1, 14, 9, -1516, 4345, 507870, -4984063, -367545880, 7749976401, 471799390490, -18036953224367, -948817553760324, 60774529797257081, 2736041193224490494, -284790488755979731455, -10493764378757426300848, 1792499910367109444364961, 49177040508763120698604578

Offset: 0

Author

Seiichi Manyama, Jun 09 2025

Keywords

• sign

Examples

			E.g.f.: A(x) = 1 - x - x^2/2 + 14*x^3/6 + 9*x^4/24 - 1516*x^5/120 + ...
A(-x*A(x)) =  1 + x - 3*x^2/2 - 11*x^3/6 + 233*x^4/24 + 621*x^5/120 - ...
		

Crossrefs

Column k=1 of A384758.

Cf. A162659, A384760.

Programs

PARI

a(n, k=1) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j)));

Formula

See A384758.