A169638 - OEIS

%I #17 Dec 26 2014 04:07:12

%S 1,1,1,4,20,60,420,3360,30240,151200,1663200,9979200,129729600,

%T 1816214400,27243216000,217945728000,3705077376000,66691392768000,

%U 633568231296000,12671364625920000,266098657144320000,5854170457175040000,134645920515025920000,1615751046180311040000

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

%H Robert Israel, <a href="/A169638/b169638.txt">Table of n, a(n) for n = 0..429</a>

%F a(n) = number of permutations of the list b[0..n] where b(0)=0 and b(n) = A005229(n) for n>=1.

%p N:= 100: # to get a(0) to a(N)

%p A005229:= proc(n) option remember;

%p procname(procname(n-2))+procname(n-procname(n-2))

%p end proc:

%p A005229(1):= 1: A005229(2):= 1:

%p V:= Vector(N):

%p A[0]:= 1: V[1]:= 1:

%p for n from 1 to N do

%p   r:= A005229(n);

%p   V[r]:= V[r]+1;

%p   A[n]:= A[n-1]*(n+1)/V[r];

%p od:

%p seq(A[i],i=0..N); # _Robert Israel_, Dec 23 2014

%t Mallows[n_Integer?Positive] := Mallows[n] = Mallows[Mallows[n - 2]] + Mallows[ n - Mallows[n - 2]];

%t Mallows[0] = Mallows[1] = Mallows[2] = 1;

%t a[m_] := Length[Permutations[Table[Mallows[i], {i, 0, m}]]];

%t Table[a[m], {m, 0, 10}]

%t (* 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 Cf. A169637.

%K nonn

%O 0,4

%A _Roger L. Bagula_, Apr 04 2010

%E Edited and new name, _Joerg Arndt_, Dec 23 2014

%E a(11) to a(23) from _Robert Israel_, Dec 23 2014