A048800 E.g.f. satisfies A(x) = 1 + x * A(x / (1 - x)).

1, 1, 2, 12, 120, 1800, 37440, 1023120, 35360640, 1502323200, 76738233600, 4629350880000, 325036115712000, 26238156161817600, 2409994778846054400, 249634150247978496000, 28935351060849192960000, 3727654806346921562112000, 530531863561703729037312000

Offset: 0

Author

Christian G. Bower, Mar 15 1999

Keywords

• nonn
• eigen

Crossrefs

Cf. A000110.

Programs

Mathematica

m = 17; A[_] = 0;
Do[A[x_] = 1 + x A[x/(1 - x)] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Oct 02 2019 *)

PARI

Vec( serlaplace( 1 + x * serlaplace( exp(exp(x) - 1)))) /* Michael Somos, Jun 14 1999 */

Sage

[factorial(m) * bell_number(m - 1) for m in range(17)]  # Zerinvary Lajos, Jul 06 2008

Formula

a(n) = n!*A000110(n-1), n>0. - Michael Somos, Jun 14 1999

Extensions

Description corrected by Michael Somos