A285424 Sum of the entries in the last blocks of all set partitions of [n].

1, 5, 19, 75, 323, 1512, 7630, 41245, 237573, 1451359, 9365361, 63604596, 453206838, 3378581609, 26285755211, 212953670251, 1792896572319, 15658150745252, 141619251656826, 1324477898999161, 12791059496663293, 127395689514237279, 1307010496324272157

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Wikipedia, Partition of a set

Example

a(3) = 19 because the sum of the entries in the last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+2+5+3 = 19.

Maple

a:= proc(h) option remember; local b; b:=
      proc(n, m, s) option remember; `if`(n=0, s,
        add(b(n-1, max(m, j), `if`(j<m, s, (h-n+1)+
        `if`(j=m, s, 0))), j=1..m+1))
      end: b(h, 0$2)
    end:
seq(a(n), n=1..25);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_, s_] := b[n, m, s] = If[n == 0, s,   Sum[b[n-1, Max[m, j], If[j < m, s, h - n + 1 + If[j == m, s, 0]]], {j, 1, m + 1}]]; b[h, 0, 0]];
Array[a, 25] (* Jean-François Alcover, May 22 2018, translated from Maple *)

Crossrefs

Cf. A285362, A285363, A285382.

Column k=1 of A286232.

Sequence in context: A149768 A149769 A149770 * A275859 A323269 A268815

Adjacent sequences: A285421 A285422 A285423 * A285425 A285426 A285427

Keyword

nonn

Author

Alois P. Heinz, Apr 18 2017

Status

approved