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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). 2
1, 1, 4, 40, 355, 4425, 69521, 1162951, 22259414, 478096938, 11614132907, 299700810545, 8456607358157, 255883964141333, 8275199908539114, 287869753459458468, 10564476589147507523, 409845503129745719513, 16777378294629533764699, 720626728499888159724831 (list; graph; refs; listen; history; text; internal format)
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);

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

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)