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A327676 Total number of colors in all 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
0, 1, 7, 96, 1120, 17133, 318550, 6174409, 134222746, 3227634290, 86758393637, 2455321082763, 75378081090618, 2465367832093301, 85698931156186485, 3188667759545387936, 124641366048950285559, 5131034234304472735967, 222142129822095164108159 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k=1..n} k * A327673(n,k).

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(k*b(n$2, i, 0)*(-1)^(k-i)*

        binomial(k, i), i=0..k), k=0..n):

seq(a(n), n=0..23);

CROSSREFS

Cf. A327673.

Sequence in context: A054932 A217240 A222834 * A338075 A177879 A090687

Adjacent sequences:  A327673 A327674 A327675 * A327677 A327678 A327679

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 21 2019

STATUS

approved

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Last modified October 25 01:39 EDT 2020. Contains 338010 sequences. (Running on oeis4.)