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%I #16 Jul 10 2015 19:30:08
%S 0,1,8,58,432,3396,28384,252456,2385280,23874448,252380800,2809461920,
%T 32841595136,402105388608,5144478074368,68625615724160,
%U 952603633463296,13735016459768064,205358227932235776,3179027634604907008,50881656554805620736,840901491722391454720,14332437167995507302400
%N Number of edges in the Hasse diagrams for the B-analogs of the partition lattices.
%H R. Suter, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/SUTER/sut1.html">Two analogues of a classical sequence</a>, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
%F E.g.f.: 1/4 * (exp(4*x)-1) * exp(1/2*exp(2*x)+x-1/2).
%t max = 18; CoefficientList[ Series[1/4*E^x*(E^(4*x) - 1)*E^((1/2)*(E^(2*x) - 1)), {x, 0, max}], x]*Range[0, max]! (* _Jean-François Alcover_, Oct 04 2013, after e.g.f. *)
%o (PARI) x='x+O('x^66); concat([0], Vec( serlaplace( 1/4*(exp(4*x)-1)*exp(1/2*exp(2*x)+x-1/2) ) ) ) \\ _Joerg Arndt_, Oct 04 2013
%Y Edges in the Hasse diagrams for partition lattices: A003128, D-analogs = A039765.
%K nonn
%O 0,3
%A Ruedi Suter (suter(AT)math.ethz.ch)
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