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A169638 Number of multiset permutations of the n initial elements of A005229 with additional element A005229(0)=1.

%I A169638 #17 Dec 26 2014 04:07:12
%S A169638 1,1,1,4,20,60,420,3360,30240,151200,1663200,9979200,129729600,
%T A169638 1816214400,27243216000,217945728000,3705077376000,66691392768000,
%U A169638 633568231296000,12671364625920000,266098657144320000,5854170457175040000,134645920515025920000,1615751046180311040000
%N A169638 Number of multiset permutations of the n initial elements of A005229 with additional element A005229(0)=1.
%H A169638 Robert Israel, <a href="/A169638/b169638.txt">Table of n, a(n) for n = 0..429</a>
%F A169638 a(n) = number of permutations of the list b[0..n] where b(0)=0 and b(n) = A005229(n) for n>=1.
%p A169638 N:= 100: # to get a(0) to a(N)
%p A169638 A005229:= proc(n) option remember;
%p A169638 procname(procname(n-2))+procname(n-procname(n-2))
%p A169638 end proc:
%p A169638 A005229(1):= 1: A005229(2):= 1:
%p A169638 V:= Vector(N):
%p A169638 A[0]:= 1: V[1]:= 1:
%p A169638 for n from 1 to N do
%p A169638   r:= A005229(n);
%p A169638   V[r]:= V[r]+1;
%p A169638   A[n]:= A[n-1]*(n+1)/V[r];
%p A169638 od:
%p A169638 seq(A[i],i=0..N); # _Robert Israel_, Dec 23 2014
%t A169638 Mallows[n_Integer?Positive] := Mallows[n] = Mallows[Mallows[n - 2]] + Mallows[ n - Mallows[n - 2]];
%t A169638 Mallows[0] = Mallows[1] = Mallows[2] = 1;
%t A169638 a[m_] := Length[Permutations[Table[Mallows[i], {i, 0, m}]]];
%t A169638 Table[a[m], {m, 0, 10}]
%t A169638 (* A much better way to compute the terms is to use the multinomials of the multiplicities of the terms of A005229! - _Joerg Arndt_, Dec 23 2014 *)
%Y A169638 Cf. A169637.
%K A169638 nonn
%O A169638 0,4
%A A169638 _Roger L. Bagula_, Apr 04 2010
%E A169638 Edited and new name, _Joerg Arndt_, Dec 23 2014
%E A169638 a(11) to a(23) from _Robert Israel_, Dec 23 2014