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A285365
Sum of the entries in the third blocks of all set partitions of [n].
2
3, 28, 185, 1094, 6293, 36619, 219931, 1376929, 9023266, 61944014, 445076570, 3341575188, 26164558199, 213243368898, 1805626838935, 15856747810014, 144189514375955, 1355629263039685, 13159535002316403, 131729480987412527, 1358188539892586220
OFFSET
3,1
LINKS
FORMULA
a(n) = A285362(n,3).
EXAMPLE
a(3) = 3 because the sum of the entries in the third blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+0+0+0+3 = 3.
MAPLE
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=3, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=3..30);
MATHEMATICA
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 3, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 3, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
CROSSREFS
Column k=3 of A285362.
Sequence in context: A302522 A303405 A074922 * A366689 A160872 A081019
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 17 2017
STATUS
approved