A327677 Number of colored compositions of n using all colors of an n-set such that any part i has a color pattern of i (distinct) colors in increasing order.

1, 1, 3, 13, 71, 481, 3861, 35743, 373591, 4347103, 55671713, 777540523, 11754153869, 191114449579, 3324296885339, 61575268263193, 1209681079172663, 25116819005925409, 549458325556099551, 12629191765880480035, 304232436498153748441, 7663883684722855430077

Offset: 0

Author

Alois P. Heinz, Sep 21 2019

Keywords

• nonn

Examples

			a(3) = 13: 3abc, 2ab1c, 2ac1b, 2bc1a, 1a2bc, 1b2ac, 1c2ab, 1a1b1c, 1a1c1b, 1b1a1c, 1b1c1a, 1c1a1b, 1c1b1a.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..444

Crossrefs

Cf. A261774.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j)*binomial(n, i*j), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..23);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0,
     Sum[b[n - i*j, i - 1, p + j]*Binomial[n, i*j], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Aug 01 2021, after Alois P. Heinz *)