A320823 Number of partitions of n with exactly ten sorts of part 1 which are introduced in ascending order.

1, 55, 1706, 39381, 754514, 12703792, 194550591, 2771831836, 37320172644, 480276118242, 5957871478583, 71707499618340, 841619253647975, 9671546736478641, 109173363429796284, 1213748225365119080, 13319241381691393856, 144529657166520849546

Offset: 10

Author

Alois P. Heinz, Oct 21 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..1006

Crossrefs

Column k=10 of A292746.

Cf. A320740, A320741.

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))(10):
seq(a(n), n=10..35);

Formula

a(n) = A320741(n) - A320740(n).