A300702 Number of compositions (ordered partitions) of n into parts that do not divide n.

1, 0, 0, 0, 0, 2, 0, 7, 2, 7, 7, 54, 2, 143, 33, 47, 30, 986, 23, 2583, 58, 1018, 828, 17710, 32, 23866, 3917, 14586, 1368, 317810, 248, 832039, 5902, 188953, 85038, 1505979, 602, 14930351, 393663, 2350986, 13524, 102334154, 16401, 267914295, 431711, 4438212, 8400611, 1836311902

Offset: 0

Author

Ilya Gutkovskiy, Mar 11 2018

Keywords

• nonn

Examples

			a(7) = 7 because we have [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2] and [2, 2, 3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000
• Index entries for sequences related to compositions

Crossrefs

Cf. A011782, A098743, A100346, A200745.

Programs

Maple

a:= proc(m) option remember; local b; b:= proc(n)
      option remember; `if`(n=0, 1, add(`if`(
      irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 11 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 47}]