A320737 Number of partitions of n with six sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 233, 965, 4425, 21904, 114910, 628754, 3544272, 20393306, 118986963, 700768255, 4152987416, 24714368292, 147480695339, 881688073414, 5277421580515, 31613933962624, 189481916086717, 1136086826214117, 6813308511956936, 40867019987219945

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1288

Crossrefs

Column k=6 of A292745.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..6), 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, 6}], 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 *)