A384760 E.g.f. A(x) satisfies A(x) = exp( -x*A(x) * A(-x*A(x)) ).

1, -1, 1, 5, -35, -281, 5671, 42671, -2179127, -9146017, 1529743051, -2876300681, -1703719191635, 19006164045023, 2748187169359087, -67807538576332801, -6002760779933693039, 267196356696377129023, 16763997717087046669459, -1258157898725874129675001

Offset: 0

Author

Seiichi Manyama, Jun 09 2025

Keywords

• sign

Examples

			E.g.f.: A(x) =  1 - x + x^2/2 + 5*x^3/6 - 35*x^4/24 - 281*x^5/120 + ...
A(x) * A(-x*A(x)) = 1 - 2*x^2/2 + 3*x^3/6 + 80*x^4/24 - 535*x^5/120 - ...
		

Crossrefs

Column k=1 of A384761.

Programs

PARI

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

Formula

See A384761.