A070289 Number of distinct values of multinomial coefficients ( n / (p1, p2, p3, ...) ) where (p1, p2, p3, ...) runs over all partitions of n.

1, 1, 2, 3, 5, 7, 11, 14, 20, 27, 36, 47, 64, 79, 102, 125, 157, 193, 243, 296, 366, 441, 538, 639, 773, 911, 1092, 1294, 1532, 1799, 2131, 2475, 2901, 3369, 3935, 4554, 5292, 6084, 7033, 8087, 9292, 10617, 12198, 13880, 15874, 18039, 20541, 23263, 26414, 29838

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..92

Sergei Viznyuk, C-Program, C-Program, local copy.

Formula

a(n) = A215520(n,n) = A215521(2*n,n). - Alois P. Heinz, Nov 08 2012

Maple

b:= proc(n, i) option remember;
      if n=0 then {1} elif i<1 then {} else {b(n, i-1)[],
         seq(map(x-> x*i!^j, b(n-i*j, i-1))[], j=1..n/i)} fi
    end:
a:= n-> nops(b(n, n)):
seq(a(n), n=0..50);  # Alois P. Heinz, Aug 14 2012

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {1}, If[i<1, {}, Union[Join[b[n, i-1], Flatten[ Table[Function[{x}, x*i!^j] /@ b[n-i*j, i-1], {j, 1, n/i}]]]]]]; a[n_] := Length[b[n, n]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 23 2015, after Alois P. Heinz *)

Prog

(Sage)
def A070289(n):
    P = Partitions(n)
    M = set(multinomial(list(x)) for x in P)
    return len(M)
[A070289(n) for n in range(20)]
# Joerg Arndt, Aug 14 2012

Crossrefs

Cf. A000041, A036038, A212855, A309951, A309999, A325305.

Sequence in context: A347572 A363068 A238864 * A035961 A051056 A055803

Adjacent sequences: A070286 A070287 A070288 * A070290 A070291 A070292

Keyword

nonn

Author

Naohiro Nomoto, May 12 2002

Extensions

Terms a(n) for n >= 45 corrected by Joerg Arndt and Alois P. Heinz, Aug 14 2012

Status

approved