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

0,3

Links

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

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 *)

Crossrefs

Column k=5 of A292745.

Sequence in context: A056783 A320735 A176697 * A320737 A320738 A320739

Adjacent sequences: A320733 A320734 A320735 * A320737 A320738 A320739

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved