A333061 Number of entries in the fourth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 11, 81, 512, 3151, 20071, 133853, 924320, 6551293, 47529561, 354259153, 2725545695, 21741995463, 180198265559, 1551865576121, 13865702570254, 128238585735637, 1224733005946425, 12053244176971825, 122035994844818345, 1269623551116437475, 13561114665253219451

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..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, 4)[2]:
seq(a(n), n=4..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, 4][[2]];
a /@ Range[4, 25] (* Jean-François Alcover, Apr 24 2021, after Alois P. Heinz *)

Crossrefs

Column k=4 of A319375.

Sequence in context: A210064 A323223 A211557 * A055429 A227556 A181989

Adjacent sequences: A333058 A333059 A333060 * A333062 A333063 A333064

Keyword

nonn

Author

Alois P. Heinz, Mar 06 2020

Status

approved