OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..92
George E. Andrews, Arnold Knopfmacher, and Burkhard Zimmermann, On the number of distinct multinomial coefficients, Journal of Number Theory 118 (2006), 15-30; arXiv preprint, arXiv:math/0509470 [math.CO], 2005.
Sergei Viznyuk, C-Program, C-Program, local copy.
FORMULA
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
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