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A325478 Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and all colors of an initial interval of the color palette are used. 2
1, 1, 4, 29, 329, 5252, 110955, 2972769, 97922354, 3872594811, 180459028989, 9759149087646, 604841170643957, 42508077480226893, 3357224252026104140, 295651782273190911233, 28834727303442640011901, 3095877335697619795977036, 363977673792652615285223095 (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), j=1..min(k, 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..23);

MATHEMATICA

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];

a[n_] := Sum[Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}], {k, 0, n}];

a /@ Range[0, 23] (* Jean-Fran├žois Alcover, Dec 14 2020, after Alois P. Heinz *)

CROSSREFS

Row sums of A322670.

Sequence in context: A295237 A028853 A118795 * A099700 A305636 A276728

Adjacent sequences:  A325475 A325476 A325477 * A325479 A325480 A325481

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 06 2019

STATUS

approved

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Last modified May 20 08:03 EDT 2022. Contains 353852 sequences. (Running on oeis4.)