A320735 Number of partitions of n with four sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 62, 217, 803, 3092, 12128, 48047, 191266, 763249, 3049383, 12190360, 48747140, 194960047, 779783252, 3119019290, 12475849884, 49902945245, 199610872683, 798441674561, 3193763066392, 12775045002551, 51100165484967, 204400632890492

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1663

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..4), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 4}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A292745.

Sequence in context: A357792 A361625 A056783 * A176697 A320736 A320737

Adjacent sequences: A320732 A320733 A320734 * A320736 A320737 A320738

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved