A350648 Sum over all partitions of [n] of the number of blocks containing their own index when blocks are ordered with decreasing largest elements.

0, 1, 1, 5, 11, 48, 173, 795, 3719, 19343, 106563, 628508, 3923602, 25875858, 179468739, 1305268102, 9925892324, 78728325373, 649856661196, 5571421770478, 49521735963376, 455616186779543, 4332419124871058, 42520560822961111, 430191406640367880

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Formula

a(n) = Sum_{k=1..ceiling(n/2)} k * A350647(n,k).

Example

a(3) = 5 = 3*1 + 2*2: 321, 3|21, 3|2|1; 31|2.
a(4) = 11 = 7*1 + 2*2: 4321, 43|21, 43|2|1, 421|3, 4|321, 4|32|1, 41|3|2; 431|2, 41|32.

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0], add((p->p+
      [0, `if`(j=n, p[1], 0)])(b(n-1, max(j, m))), j=1..m+1))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, p + {0, If[j == n, p[[1]], 0]}][b[n - 1, Max[j, m]]], {j, 1, m + 1}]];
a[n_] := b[n, 0][[2]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 11 2022, after Alois P. Heinz *)

Crossrefs

Cf. A350589, A350647.

Sequence in context: A149513 A327494 A097743 * A176609 A041213 A142238

Adjacent sequences: A350645 A350646 A350647 * A350649 A350650 A350651

Keyword

nonn

Author

Alois P. Heinz, Jan 09 2022

Status

approved