A320736 Number of partitions of n with five sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 232, 944, 4158, 19236, 91794, 446311, 2194569, 10863768, 53995350, 269013587, 1342192961, 6702368648, 33486112079, 167353481065, 836536395240, 4181989400979, 20907870188551, 104533122311131, 522646929294281, 2613178606952285

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1433

Crossrefs

Column k=5 of A292745.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..5), 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, 5}], 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 *)