cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A285365 Sum of the entries in the third blocks of all set partitions of [n].

Original entry on oeis.org

3, 28, 185, 1094, 6293, 36619, 219931, 1376929, 9023266, 61944014, 445076570, 3341575188, 26164558199, 213243368898, 1805626838935, 15856747810014, 144189514375955, 1355629263039685, 13159535002316403, 131729480987412527, 1358188539892586220
Offset: 3

Views

Author

Alois P. Heinz, Apr 17 2017

Keywords

Examples

			a(3) = 3 because the sum of the entries in the third blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+0+0+0+3 = 3.
		

Crossrefs

Column k=3 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=3, 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=3..30);
  • Mathematica
    a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 3, 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, 3, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Formula

a(n) = A285362(n,3).