A270501 Sum of the sizes of the ninth blocks in all set partitions of {1,2,...,n}.

1, 47, 1267, 25820, 443249, 6782968, 95737722, 1274661371, 16262852622, 201150251360, 2433394489974, 28994047438464, 342194356303003, 4019284858043011, 47169786677194389, 555004306379162344, 6566292430043177959, 78313245092235242824, 943595956075419339524

Offset: 9

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..575
• Wikipedia, Partition of a set

Crossrefs

Column p=9 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<10, [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, 9):
seq(a(n), n=9..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 10, {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, 9];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)