A332942 Number of entries in the second blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 7, 25, 101, 366, 1555, 7099, 34627, 184033, 1059972, 6425992, 41266681, 280938451, 2009636335, 15025372685, 117386912433, 956458929950, 8104399834719, 71244441818927, 648761935841876, 6110827367541999, 59454153443971106, 596654820386392152

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..576

Wikipedia, Partition of a set

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
      max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
    end:
a:= n-> b(n, 1, 2)[2]:
seq(a(n), n=2..24);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i > n, 0 {0, 0}, Sum[ Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i}, {0, 0}]][b[n - i*j, i + 1, Max[0, t - j]]/j!*multinomial[n, Append[Table[i, {j}], n - i*j]]], {j, 0, n/i}]]];
a[n_] := b[n, 1, 2][[2]];
a /@ Range[2, 24] (* Jean-François Alcover, Jan 06 2021, after Alois P. Heinz *)

Crossrefs

Column k=2 of A319298.

Sequence in context: A304421 A138729 A035509 * A247173 A141627 A289606

Adjacent sequences: A332939 A332940 A332941 * A332943 A332944 A332945

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2020

Status

approved