A004121 - OEIS

%I M2095 #26 Jan 31 2022 01:27:54

%S 2,16,208,3968,109568,4793344,410662912,82657083392,38274970222592,

%T 37590755515826176,75458309991776124928,305873605165090925969408,

%U 2491832958314452159507202048,40704585435508852018947014262784

%N Generalized weak orders on n points.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D C. G. Wagner, Enumeration of generalized weak orders. Arch. Math. (Basel) 39 (1982), no. 2, 147-152.

%H Vincenzo Librandi, <a href="/A004121/b004121.txt">Table of n, a(n) for n = 1..80</a>

%H C. G. Wagner, <a href="/A004121/a004121_1.pdf">Enumeration of generalized weak orders</a>, Preprint, 1980. [Annotated scanned copy]

%H C. G. Wagner and N. J. A. Sloane, <a href="/A004121/a004121.pdf">Correspondence, 1980</a>

%F E.g.f.: 1/(1 - Sum_{i >= 1} 2^binomial(i+1, 2)*x^i/i!).

%t max = 14; f[x_] := 1/(1 - Sum[(2^(i*(i+1)/2)*x^i)/i!, {i, 1, max}]); Drop[ CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!, 1] (* _Jean-François Alcover_, Oct 21 2011, after g.f. *)

%Y Cf. A004122, A004123, A000670 (asymmetric generalized weak orders on n points).

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_

%E Formula and more terms from _Vladeta Jovovic_, Mar 27 2001