A346772 Total sum of block indices of the elements over all partitions of [n].

0, 1, 5, 22, 100, 482, 2475, 13527, 78476, 481687, 3117962, 21218851, 151387882, 1129430737, 8790433999, 71222812912, 599577147056, 5235054113412, 47331036294905, 442462325254995, 4270909302907430, 42514043248222709, 435920900603529954, 4599155199953703373

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..574

Wikipedia, Partition of a set

Formula

a(n) = Sum_{k=1..n} A120057(n,k).

a(n) = Sum_{k=0..n*(n-1)/2} (n+k) * A126347(n,k).

a(n) = Sum_{k=1..n} k * A270236(n,k).

Example

a(3) = 22 = 3 + 4 + 4 + 5 + 6, summing block indices 111, 112, 121, 122, 123 of the 5 partitions of [3]: 123, 12|3, 13|2, 1|23, 1|2|3.

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0], add(
     (p-> p+[0, p[1]*j])(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[
     Function[p, p+{0, p[[1]]*j}][b[n-1, Max[m, j]]], {j, 1, m+1}]];
a[n_] := b[n, 0][[2]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 27 2022, after Alois P. Heinz *)

Crossrefs

Row sums of A120057.

Cf. A000110, A070071, A105488, A126347, A270236.

Sequence in context: A123347 A087439 A033452 * A295519 A179602 A262440

Adjacent sequences: A346769 A346770 A346771 * A346773 A346774 A346775

Keyword

nonn

Author

Alois P. Heinz, Aug 02 2021

Status

approved