A285363 Sum of the entries in the first blocks of all set partitions of [n].

1, 4, 15, 60, 262, 1243, 6358, 34835, 203307, 1257913, 8216945, 56463487, 406868167, 3065920770, 24099977863, 197179545722, 1675846476148, 14769104672839, 134745258569108, 1270767279092285, 12371426210292311, 124173909409948575, 1283498833928098171

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..575

Wikipedia, Partition of a set

Formula

a(n) = A285362(n,1).

Example

a(3) = 15 because the sum of the entries in the first blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+4+1+1 = 15.

Maple

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

Mathematica

a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[If[j == 1, # + {0, (h - n + 1)*#[[1]]}, #]&[b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, May 20 2018, translated from Maple *)

Crossrefs

Column k=1 of A285362.

Cf. A284816, A285424.

Sequence in context: A290910 A369838 A070071 * A356942 A151484 A275871

Adjacent sequences: A285360 A285361 A285362 * A285364 A285365 A285366

Keyword

nonn

Author

Alois P. Heinz, Apr 17 2017

Status

approved