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A270495 Sum of the sizes of the third blocks in all set partitions of {1,2,...,n}. 2
1, 8, 47, 253, 1345, 7304, 41193, 243152, 1506521, 9799547, 66844755, 477297022, 3560469469, 27692022408, 224128400923, 1884299045789, 16427961558365, 148293477761232, 1384008870213057, 13336887952918752, 132535336519342301, 1356662080571809755 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..575

Wikipedia, Partition of a set

MAPLE

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

      add((p->`if`(j<4, [p[1], p[2]+p[1]*x^j], p))(

       b(n-1, max(m, j))), j=1..m+1))

    end:

a:= n-> coeff(b(n, 0)[2], x, 3):

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

MATHEMATICA

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 4, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];

a[n_] := Coefficient[b[n, 0][[2]], x, 3];

Table[a[n], {n, 3, 25}] (* Jean-Fran├žois Alcover, May 27 2018, translated from Maple *)

CROSSREFS

Column p=3 of A270236.

Sequence in context: A139262 A026900 A016198 * A177257 A051140 A296631

Adjacent sequences:  A270492 A270493 A270494 * A270496 A270497 A270498

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 18 2016

STATUS

approved

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)