A285371 Sum of the entries in the ninth blocks of all set partitions of [n].

9, 460, 13365, 291312, 5313419, 85887795, 1273861815, 17739276489, 235727269842, 3025136223480, 37838768653358, 464684701656546, 5636371498958757, 67862072916294706, 814494099000392487, 9780912755503955712, 117894823818639390505, 1430383074839724093993

Offset: 9

Author

Alois P. Heinz, Apr 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..400
• Wikipedia, Partition of a set

Crossrefs

Column k=9 of A285362.

Programs

Maple

a:= proc(h) option remember; local b; b:=
      proc(n, m) option remember;
        `if`(n=0, [1, 0], add((p-> `if`(j=9, 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=9..30);

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 9, 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, 9, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A285362(n,9).