A039765 Number of edges in the Hasse diagrams for the D-analogs of the partition lattices.

0, 0, 4, 31, 240, 1931, 16396, 147589, 1408224, 14214559, 151394940, 1696783221, 19958826080, 245788962199, 3161635135340, 42390110260685, 591257152058944, 8563898444592927, 128598641049231996

Offset

0,3

Links

Table of n, a(n) for n=0..18.

R. Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.

Formula

E.g.f.: f_4(x)*g_1(x)*e_1(f_2(x)) + e_1(x)*g_4(x)*e_1(g_2(x)) where e_n(x) = 1/n exp(n x); f_n(x) = 1/n (exp(n x) - 1); g_n(x) = 1/n (exp(n x) - 1 - n x).

Mathematica

max = 18; e[n_, x_] := E^(n*x)/n; f[n_, x_] := (E^(n*x) - 1)/n; g[n_, x_] := (E^(n*x) - 1 - n*x)/n; se = Series[ f[4, x]*g[1, x]*e[1, f[2, x]] + e[1, x]*g[4, x]*e[1, g[2, x]], {x, 0, max}]; CoefficientList[se, x]*Range[0, max]! (* Jean-François Alcover, May 04 2012, after e.g.f. *)

Crossrefs

Edges in the Hasse diagrams for partition lattices: A003128, B-analogs = A039759.

Sequence in context: A014537 A136284 A183911 * A001091 A309184 A077615

Adjacent sequences: A039762 A039763 A039764 * A039766 A039767 A039768

Keyword

nonn,nice

Author

Ruedi Suter (suter(AT)math.ethz.ch)

Status

approved