A048800 - OEIS

%I #23 Sep 22 2025 16:00:32

%S 1,1,2,12,120,1800,37440,1023120,35360640,1502323200,76738233600,

%T 4629350880000,325036115712000,26238156161817600,2409994778846054400,

%U 249634150247978496000,28935351060849192960000,3727654806346921562112000,530531863561703729037312000

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

%F a(n) = n!*A000110(n-1), n>0. - _Michael Somos_, Jun 14 1999

%t m = 17; A[_] = 0;

%t Do[A[x_] = 1 + x A[x/(1 - x)] + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x]*Range[0, m - 1]! (* _Jean-François Alcover_, Oct 02 2019 *)

%o (PARI) Vec( serlaplace( 1 + x * serlaplace( exp(exp(x) - 1)))) /* _Michael Somos_, Jun 14 1999 */

%o (SageMath) [factorial(m) * bell_number(m - 1) for m in range(17)]  # _Zerinvary Lajos_, Jul 06 2008

%Y Cf. A000110.

%K nonn,eigen

%O 0,3

%A _Christian G. Bower_, Mar 15 1999

%E Description corrected by _Michael Somos_