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A327680 Total number of colors used in all colored integer partitions of n using all colors of an initial interval of the color palette such that parts i have distinct color patterns in arbitrary order and each pattern for a part i has i colors in (weakly) increasing order. 2
0, 1, 7, 44, 358, 2904, 29112, 296448, 3520568, 43482208, 602603120, 8712724080, 138736978208, 2302036052128, 41417364992160, 776413790063328, 15597709327298944, 325945020056535968, 7238587734613470208, 166897326948551436384, 4061690336695535982048 (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 * A309973(n,k).

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1,

      `if`(i<1, 0, add(b(n-i*j, min(n-i*j, i-1), k)*

       binomial(binomial(k+i-1, i), j)*j!, j=0..n/i)))

    end:

a:= n-> add(add(k*b(n$2, i)*(-1)^(k-i)*

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

seq(a(n), n=0..22);

CROSSREFS

Cf. A309973.

Sequence in context: A091127 A166775 A221541 * A156374 A171493 A262772

Adjacent sequences:  A327677 A327678 A327679 * A327681 A327682 A327683

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 21 2019

STATUS

approved

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)