A333062 Number of entries in the fifth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 16, 162, 1345, 10096, 72973, 531015, 3984762, 30987321, 248303940, 2036778980, 17044330217, 145588640408, 1272940217747, 11434350878640, 105849240653792, 1011701166471075, 9987958951272492, 101765834737586068, 1068365602976497915, 11534318293877771406

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..576

Wikipedia, Partition of a set

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
       combinat[multinomial](n, i$j, n-i*j)/j!*
      b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
    end:
a:= n-> b(n$2, 5)[2]:
seq(a(n), n=5..25);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[
     Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i}, {0, 0}]][
     multinomial[n, Append[Table[i, {j}], n - i*j]]/j!*
     b[n - i*j, Min[n - i*j, i - 1], Max[0, t - j]]], {j, 0, n/i}]]];
a[n_] := b[n, n, 5][[2]];
a /@ Range[5, 25] (* Jean-François Alcover, Apr 24 2021, after Alois P. Heinz *)

Crossrefs

Column k=5 of A319375.

Sequence in context: A371195 A259547 A211558 * A208311 A232333 A091363

Adjacent sequences: A333059 A333060 A333061 * A333063 A333064 A333065

Keyword

nonn

Author

Alois P. Heinz, Mar 06 2020

Status

approved