OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..697
Wikipedia, Multinomial coefficients
FORMULA
EXAMPLE
a(10) = 12600 = 10! / (4! * 3! * 2! * 1!) is the value for partition [4,3,2,1]. All other partitions of 10 into distinct parts give smaller values: [5,3,2]-> 2520, [5,4,1]-> 1260, [6,3,1]-> 840, [6,4]-> 210, [7,2,1]-> 360, [7,3]-> 120, [8,2]-> 45, [9,1]-> 10, [10]-> 1.
MAPLE
b:= proc(n, i) option remember; `if`(n>i*(i+1)/2, infinity,
`if`(n=0, 1, min(b(n, i-1), b(n-i, min(n-i, i-1))*i!)))
end:
a:= n-> n!/b(n$2):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*n/
(t-> t*(t+3)/2-n+2)(floor(sqrt(8*n-7)/2-1/2)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Aug 05 2017
MATHEMATICA
b[n_, i_]:=b[n, i]=If[n>i*(i + 1)/2, Infinity, If[n==0, 1, Min[b[n, i - 1], b[n - i, Min[n - i, i - 1]]*i!]]]; Table[n!/b[n, n], {n, 0, 30}] (* Indranil Ghosh, Aug 05 2017, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 04 2017
STATUS
approved