OFFSET
0,5
COMMENTS
The ordering of integer partitions used in this version is also called:
- canonical ordering
- graded reverse lexicographic ordering
- magma (software) ordering
by opposition to the ordering used by Abramowitz and Stegun.
LINKS
Alois P. Heinz, Rows n = 0..28, flattened
EXAMPLE
First rows are:
1
1
1 1
2 3 1
6 8 3 6 1
24 30 20 20 15 10 1
120 144 90 90 40 120 40 15 45 15 1
720 840 504 504 420 630 210 280 210 420 70 105 105 21 1
...
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1],
`if`(i<1, [], [seq(map(x-> x*i^j*j!,
b(n-i*j, i-1))[], j=[iquo(n, i)-t$t=0..n/i])]))
end:
T:= n-> map(x-> n!/x, b(n$2))[]:
seq(T(n), n=0..10); # Alois P. Heinz, Dec 04 2016
MATHEMATICA
Flatten[Table[
Map[n!/Times @@ ((First[#]^Length[#]*Factorial[Length[#]]) & /@
Split[#]) &, IntegerPartitions[n]], {n, 1, 8}]]
(* Second program: *)
b[n_, i_] := b[n, i] = If[n == 0, {1},
If[i < 1, {}, Flatten@Table[#*i^j*j!& /@
b[n - i*j, i - 1], {j, Quotient[n, i] - Range[0, n/i]}]]];
T[n_] := n!/#& /@ b[n, n];
T /@ Range[0, 10] // Flatten (* Jean-François Alcover, Jun 01 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
AUTHOR
David W. Wilson and Olivier Gérard, Dec 04 2016
EXTENSIONS
One term for row n=0 prepended by Alois P. Heinz, Dec 04 2016
STATUS
approved