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

0,3

Links

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

Example

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

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 *)

Crossrefs

Cf. A261774.

Sequence in context: A111140 A302699 A137983 * A307005 A059032 A214812

Adjacent sequences: A327674 A327675 A327676 * A327678 A327679 A327680

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2019

Status

approved