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

1, 1, 1, 4, 20, 60, 420, 3360, 30240, 151200, 1663200, 9979200, 129729600, 1816214400, 27243216000, 217945728000, 3705077376000, 66691392768000, 633568231296000, 12671364625920000, 266098657144320000, 5854170457175040000, 134645920515025920000, 1615751046180311040000

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..429

Formula

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

Maple

N:= 100: # to get a(0) to a(N)
A005229:= proc(n) option remember;
procname(procname(n-2))+procname(n-procname(n-2))
end proc:
A005229(1):= 1: A005229(2):= 1:
V:= Vector(N):
A[0]:= 1: V[1]:= 1:
for n from 1 to N do
  r:= A005229(n);
  V[r]:= V[r]+1;
  A[n]:= A[n-1]*(n+1)/V[r];
od:
seq(A[i], i=0..N); # Robert Israel, Dec 23 2014

Mathematica

Mallows[n_Integer?Positive] := Mallows[n] = Mallows[Mallows[n - 2]] + Mallows[ n - Mallows[n - 2]];
Mallows[0] = Mallows[1] = Mallows[2] = 1;
a[m_] := Length[Permutations[Table[Mallows[i], {i, 0, m}]]];
Table[a[m], {m, 0, 10}]
(* 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 *)

Crossrefs

Cf. A169637.

Sequence in context: A355990 A169637 A356012 * A226424 A225260 A131479

Adjacent sequences: A169635 A169636 A169637 * A169639 A169640 A169641

Keyword

nonn

Author

Roger L. Bagula, Apr 04 2010

Extensions

Edited and new name, Joerg Arndt, Dec 23 2014

a(11) to a(23) from Robert Israel, Dec 23 2014

Status

approved