A052862 Expansion of e.g.f. log(-1/(-2+exp(x)))*x.

0, 0, 2, 6, 24, 130, 900, 7574, 74928, 851274, 10916700, 155919742, 2453941512, 42188446898, 786563892660, 15805750451430, 340522975054176, 7829628493247002, 191363568551328780, 4954089147107164238

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

A simple grammar.

For n > 2, a(n) = 2 * n * A000670(n-2). - Gerald McGarvey, Nov 01 2007 [corrected by Seiichi Manyama, May 26 2022]

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..425
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 830

Crossrefs

Cf. A000629, A000670, A354413.

Programs

Maple

spec := [S,{B=Cycle(C),C=Set(Z,1 <= card),S=Prod(Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)*((i+r)^(n-r)/(i!*(k-i-r)!)), {i, 0, k-r}], {k, r, n}];
Fubini[0, 1] = 1;
a[n_] := If[n == 2, 2, 2 n * Fubini[n-2, 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Oct 11 2022 *)

PARI

my(x='x+O('x^25)); concat([0,0],Vec(serlaplace(log(-1/(-2+exp(x)))*x))) \\ Joerg Arndt, Oct 11 2022

Formula

a(n) ~ (n-1)! / log(2)^(n-1). - Vaclav Kotesovec, Aug 04 2014