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

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A292745.

Programs

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 *)