A320734 Number of partitions of n with three sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 19, 52, 151, 442, 1314, 3921, 11737, 35171, 105464, 316318, 948863, 2846461, 8539221, 25617443, 76852054, 230555794, 691666924, 2075000173, 6224999772, 18674998357, 56024993883, 168074980137, 504224938548, 1512674813304, 4538024437036

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2097

Crossrefs

Column k=3 of A292745.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..3), 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, 3}], 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 *)