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A130907 E.g.f.: exp(x+x^2/2)/(1-x).

%I A130907 #29 Aug 13 2025 10:18:46
%S A130907 1,2,6,22,98,516,3172,22436,180252,1624888,16258376,178877832,
%T A130907 2146674136,27907332272,390705042288,5860585983856,93769421948432,
%U A130907 1594080384922656,28693447925921632,545175515402212448,10903510331802913056,228973717087813867072
%N A130907 E.g.f.: exp(x+x^2/2)/(1-x).
%C A130907 A jeweler creates collections of necklaces using exactly n different colored beads (to make the entire collection) then chooses some (or none or all) of the necklaces to sell. - _Geoffrey Critzer_, Apr 20 2009
%H A130907 Vincenzo Librandi, <a href="/A130907/b130907.txt">Table of n, a(n) for n = 0..200</a>
%F A130907 a(n) = n! + n!*Sum_{m=0..n} Sum_{k=1..m} binomial(k,m-k)*2^(k-m)/k!. - _Vladimir Kruchinin_, Jul 02 2011
%F A130907 From _Vaclav Kotesovec_, Oct 20 2012: (Start)
%F A130907 D-finite with recurrence a(n) = (n+1)*a(n-1) - (n-2)*(n-1)*a(n-3).
%F A130907 a(n) ~ n!*exp(3/2). (End)
%t A130907 CoefficientList[Series[Exp[x + x^2/2 - Log[1 - x]], {x, 0, 21}], x]* Table[n!, {n, 0, 21}] (* _Geoffrey Critzer_, Apr 20 2009 *)
%o A130907 (PARI) x='x+O('x^66);
%o A130907 egf=exp(x+x^2/2)/(1-x);
%o A130907 Vec(serlaplace(egf)) /* _Joerg Arndt_, Jul 11 2011 */
%Y A130907 Cf. A130905.
%K A130907 nonn
%O A130907 0,2
%A A130907 _Karol A. Penson_, Jun 08 2007
%E A130907 I deleted the initial 1. - _Geoffrey Critzer_, Apr 19 2009