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A332943 Number of entries in the third blocks of all set partitions of [n] when blocks are ordered by increasing lengths. 2
1, 13, 71, 396, 1877, 9199, 47371, 253108, 1420475, 8598976, 55100124, 369764734, 2614650820, 19473708445, 151503397725, 1226996194292, 10339319950504, 90530421514787, 821670728202320, 7714779905351852, 74815825933883534, 748526174347790448, 7717807072187843156 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..576

Wikipedia, Partition of a set

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,

      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,

      max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))

    end:

a:= n-> b(n, 1, 3)[2]:

seq(a(n), n=3..25);

CROSSREFS

Column k=3 of A319298.

Sequence in context: A158941 A128003 A060103 * A141989 A159512 A104132

Adjacent sequences:  A332940 A332941 A332942 * A332944 A332945 A332946

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2020

STATUS

approved

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Last modified October 25 10:46 EDT 2021. Contains 348239 sequences. (Running on oeis4.)