A320819 Number of partitions of n with exactly six sorts of part 1 which are introduced in ascending order.

1, 21, 267, 2668, 23116, 182443, 1349703, 9529538, 64991613, 431754668, 2810794455, 18011999644, 113994583260, 714334592349, 4440885185275, 27431944561645, 168574045898166, 1031553703902986, 6290661582662655, 38253841380267660, 232085126723073278

Offset: 6

Author

Alois P. Heinz, Oct 21 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1288

Crossrefs

Column k=6 of A292746.

Cf. A320736, A320737.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
    end:
a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(6):
seq(a(n), n=6..35);

Formula

a(n) = A320737(n) - A320736(n).