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A300702
Number of compositions (ordered partitions) of n into parts that do not divide n.
6
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
0,6
EXAMPLE
a(7) = 7 because we have [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2] and [2, 2, 3].
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 11 2018
STATUS
approved