A320817 Number of partitions of n with exactly four sorts of part 1 which are introduced in ascending order.

1, 10, 66, 361, 1778, 8207, 36310, 156095, 657785, 2733065, 11241497, 45900679, 186420826, 754165809, 3042167236, 12245294090, 49211278321, 197535872510, 792216674789, 3175088068035, 12719020008668, 50932090504830, 203896407951944, 816089798651203

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1663

Formula

a(n) = A320735(n) - A320734(n).

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))(4):
seq(a(n), n=4..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, k}], Sum[b[n - i*j, i - 1, k], {j, 0, n/i}]];
a[n_] := With[{k = 4}, b[n, n, k] - b[n, n, k-1]];
a /@ Range[4, 35] (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A292746.

Cf. A320734, A320735.

Sequence in context: A024391 A074362 A080421 * A004310 A026853 A177452

Adjacent sequences: A320814 A320815 A320816 * A320818 A320819 A320820

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved