A320738 Number of partitions of n with seven sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 233, 966, 4453, 22367, 120819, 693233, 4178068, 26179581, 169020426, 1115994109, 7491323062, 50893512269, 348746702822, 2404544709055, 16651752622351, 115675136440751, 805342277995251, 5615683405472021, 39202038270665250, 273878789880840798

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1187

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..7), 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, 7}], 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=7 of A292745.

Sequence in context: A176697 A320736 A320737 * A320739 A320740 A320741

Adjacent sequences: A320735 A320736 A320737 * A320739 A320740 A320741

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved