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

%I A052862 #29 Oct 11 2022 07:39:04
%S A052862 0,0,2,6,24,130,900,7574,74928,851274,10916700,155919742,2453941512,
%T A052862 42188446898,786563892660,15805750451430,340522975054176,
%U A052862 7829628493247002,191363568551328780,4954089147107164238
%N A052862 Expansion of e.g.f. log(-1/(-2+exp(x)))*x.
%C A052862 A simple grammar.
%C A052862 For n > 2, a(n) = 2 * n * A000670(n-2). - _Gerald McGarvey_, Nov 01 2007 [corrected by _Seiichi Manyama_, May 26 2022]
%H A052862 Seiichi Manyama, <a href="/A052862/b052862.txt">Table of n, a(n) for n = 0..425</a>
%H A052862 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=830">Encyclopedia of Combinatorial Structures 830</a>
%F A052862 a(n) ~ (n-1)! / log(2)^(n-1). - _Vaclav Kotesovec_, Aug 04 2014
%p A052862 spec := [S,{B=Cycle(C),C=Set(Z,1 <= card),S=Prod(Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052862 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}];
%t A052862 Fubini[0, 1] = 1;
%t A052862 a[n_] := If[n == 2, 2, 2 n * Fubini[n-2, 1]];
%t A052862 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Oct 11 2022 *)
%o A052862 (PARI) my(x='x+O('x^25)); concat([0,0],Vec(serlaplace(log(-1/(-2+exp(x)))*x))) \\ _Joerg Arndt_, Oct 11 2022
%Y A052862 Cf. A000629, A000670, A354413.
%K A052862 easy,nonn
%O A052862 0,3
%A A052862 encyclopedia(AT)pommard.inria.fr, Jan 25 2000