Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #55 Sep 08 2022 08:44:50
%S 0,1,3,14,90,744,7560,91440,1285200,20603520,371226240,7428153600,
%T 163459296000,3923502105600,102017281766400,2856571067750400,
%U 85698439706880000,2742370993410048000,93240969463369728000,3356681303055015936000,127554011161191014400000
%N a(n) = (n-1)!*(2^n-1) for n>=1, a(0)=0.
%C Labeled octupi with n nodes.
%C a(n) is the number of connected endofunctions on n points such that every nonrecurrent element has at most one element in its preimage and every recurrent element has at most two elements in its preimage. - _Geoffrey Critzer_, Dec 07 2011
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, pp. 12, 55, 409.
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.5.
%H G. C. Greubel, <a href="/A029767/b029767.txt">Table of n, a(n) for n = 0..400</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=498">Encyclopedia of Combinatorial Structures 498</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=777">Encyclopedia of Combinatorial Structures 777</a>
%F E.g.f.: log(1-x)-log(1-2*x).
%F In Maple notation, representation as an infinite sum: a(n) = sum((n+k)!/((k+1)! *2^k), k=0..infinity)/2, n=1, 2... Representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*1/2*exp(-x)/x*(2*exp(1/2*x)-2), x=0..infinity), n=1, 2... - _Karol A. Penson_, Oct 15 2002
%F D-finite with recurrence: a(n) +3*(-n+1)*a(n-1) +2*(n-1)*(n-2)*a(n-2) = 0. - _R. J. Mathar_, Jan 08 2013
%F a(n) = n!*Sum_{k=0..n-1} binomial(n-1,k)/(k+1). - _J. M. Bergot_, Jul 30 2015
%F a(n) = (1/zeta(n)) * Integral_{x=0..1} (log(1/x))^(n-1) / (sqrt(x) * (1-x)) dx. - _Amrik Singh Nimbran_, May 06 2018
%p with(combinat): seq(stirling1(j,1)*stirling2(j+1,2)*(-1)^(j+1), j=0..16); # _Zerinvary Lajos_, Mar 30 2007
%t a=x/(1-x); Range[0,20]! CoefficientList[Series[Log[1/(1-a)], {x,0,20}], x] (* _Geoffrey Critzer_, Dec 07 2011 *)
%t Join[{0}, Table[(n - 1)! (2^n - 1), {n, 20}]] (* _Vincenzo Librandi_, Apr 18 2015 *)
%o (Magma) [0] cat [Factorial(n-1)*(2^n-1): n in [1..20]]; // _Vincenzo Librandi_, Apr 18 2015
%o (PARI) concat([0], for(n=1,25, print1((n-1)!*(2^n -1), ", "))) \\ _G. C. Greubel_, Jan 19 2017
%o (GAP) Concatenation([0],List([1..20],n->Factorial(n-1)*(2^n-1))); # _Muniru A Asiru_, Aug 09 2018
%Y Cf. A001865.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_