A350683 Total sum over all partitions of [n] of elements i contained in block i when blocks are ordered with decreasing largest elements.

0, 1, 1, 8, 17, 98, 362, 1916, 9512, 53858, 315872, 1984979, 13105685, 91128546, 663815424, 5055622309, 40148341135, 331753228115, 2846786927873, 25323311882074, 233137061978065, 2218141402504254, 21780561656373552, 220451321425101091, 2297330116404668422

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..575

Wikipedia, Partition of a set

Formula

a(n) = Sum_{k=1..max(0,A008805(n-1))} k * A350684(n,k).

Example

a(4) = 17 = 3*1 + 4*2 + 2*3: 432(1), 42(1)|3, 4(1)|3|2, 43|(2)1, 43|(2)|1, 4|3(2)1, 4|3(2)|1, 43(1)|(2), 4(1)|3(2).

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0], add((p-> [0,
     `if`(n=j, p[1]*j, 0)]+p)(b(n-1, max(m, j))), j=1..m+1))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..25);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[With[{p = b[n-1, Max[m, j]]},
     {0, If[n == j, p[[1]]*j, 0]} + p], {j, 1, m+1}]];
a[n_] := b[n, 0][[2]];
Table[a[n], {n, 0, 25}]; (* Jean-François Alcover, May 08 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008805, A350648, A350684.

Sequence in context: A228684 A171065 A134790 * A177129 A177178 A357678

Adjacent sequences: A350680 A350681 A350682 * A350684 A350685 A350686

Keyword

nonn

Author

Alois P. Heinz, Jan 11 2022

Status

approved