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A325888 Number of colored set partitions of [n] where colors of the elements of subsets are in (weakly) increasing order and all colors of an initial interval of the color palette are used. 2
1, 1, 5, 41, 505, 8597, 191457, 5364837, 183744421, 7521913845, 361544182917, 20109571623693, 1278810836639233, 92032189911692253, 7430335604308535497, 667922294225164998677, 66407623510409091454229, 7260203111052685954056549, 868289612454444952122790277 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..296

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*

      binomial(n-1, j-1)*binomial(k+j-1, j), j=1..n))

    end:

a:= n-> add(add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k), k=0..n):

seq(a(n), n=0..21);

CROSSREFS

Row sums of A321296.

Sequence in context: A240996 A143415 A056545 * A275787 A009755 A000685

Adjacent sequences:  A325885 A325886 A325887 * A325889 A325890 A325891

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 07 2019

STATUS

approved

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Last modified November 12 16:45 EST 2019. Contains 329058 sequences. (Running on oeis4.)