A285372 Sum of the entries in the tenth blocks of all set partitions of [n].

10, 616, 21318, 547857, 11676343, 218761153, 3732864275, 59392240551, 895833879036, 12967143328027, 181820930739504, 2487908867278337, 33420903985242540, 442951837401015291, 5816787707500820380, 75959640100454216760, 989568067595589010921

Offset

10,1

Links

Alois P. Heinz, Table of n, a(n) for n = 10..400

Wikipedia, Partition of a set

Formula

a(n) = A285362(n,10).

Maple

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

Mathematica

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

Crossrefs

Column k=10 of A285362.

Sequence in context: A364515 A006441 A042751 * A308145 A159622 A115692

Adjacent sequences: A285369 A285370 A285371 * A285373 A285374 A285375

Keyword

nonn

Author

Alois P. Heinz, Apr 17 2017

Status

approved