A327675 Number of colored compositions of n using all colors of an initial interval of the color palette such that all parts have different color patterns and the patterns for parts i are sorted and have i colors (in arbitrary order).

1, 1, 4, 40, 355, 4425, 69521, 1162951, 22259414, 478096938, 11614132907, 299700810545, 8456607358157, 255883964141333, 8275199908539114, 287869753459458468, 10564476589147507523, 409845503129745719513, 16777378294629533764699, 720626728499888159724831

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Maple

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

Mathematica

b[n_, i_, k_, p_] := b[n, i, k, p] =
     If[n == 0, p!, If[i < 1, 0, Sum[ Binomial[k^i, j]*
     b[n - i*j, Min[n - i*j, i - 1], k, p + j]/j!, {j, 0, n/i}]]];
a[n_] := Sum[Sum[b[n, n, i, 0]*(-1)^(k - i)*
     Binomial[k, i], {i, 0, k}], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *)

Crossrefs

Row sums of A327673.

Sequence in context: A069721 A223176 A279574 * A191681 A222273 A220366

Adjacent sequences: A327672 A327673 A327674 * A327676 A327677 A327678

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2019

Status

approved