A270500 Sum of the sizes of the eighth blocks in all set partitions of {1,2,...,n}.

1, 38, 842, 14303, 207186, 2704647, 32890525, 380797185, 4261887992, 46630717274, 503083676180, 5388429971042, 57614949228381, 617784630625192, 6668316674283818, 72685580775510461, 802184346241503206, 8983104653288906449, 102246823195952449865

Offset: 8

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..575
• Wikipedia, Partition of a set

Crossrefs

Column p=8 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<9, [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, 8):
seq(a(n), n=8..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 9, {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, 8];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)