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A242882
Number of compositions of n into parts with distinct multiplicities.
64
1, 1, 2, 2, 6, 12, 16, 40, 60, 82, 216, 538, 788, 2034, 3740, 6320, 13336, 27498, 42936, 93534, 173520, 351374, 734650, 1592952, 3033194, 6310640, 12506972, 25296110, 49709476, 101546612, 195037028, 391548336, 764947954, 1527004522, 2953533640, 5946359758
OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..264 (terms 0..200 from Alois P. Heinz)
EXAMPLE
a(0) = 1: the empty composition.
a(1) = 1: [1].
a(2) = 2: [1,1], [2].
a(3) = 2: [1,1,1], [3].
a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [2,1,1], [2,2], [4].
a(5) = 12: [1,1,1,1,1], [1,1,1,2], [1,1,2,1], [1,2,1,1], [2,1,1,1], [1,2,2], [2,1,2], [2,2,1], [1,1,3], [1,3,1], [3,1,1], [5].
MAPLE
b:= proc(n, i, s) option remember; `if`(n=0, add(j, j=s)!,
`if`(i<1, 0, add(`if`(j>0 and j in s, 0,
b(n-i*j, i-1, `if`(j=0, s, s union {j}))/j!), j=0..n/i)))
end:
a:= n-> b(n$2, {}):
seq(a(n), n=0..45);
MATHEMATICA
b[n_, i_, s_] := b[n, i, s] = If[n == 0, Sum[j, {j, s}]!, If[i < 1, 0, Sum[If[j > 0 && MemberQ[s, j], 0, b[n - i*j, i - 1, If[j == 0, s, s ~Union~ {j}]]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, {}];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
PROG
(PARI) a(n)={((r, k, b, w)->if(!k||!r, if(r, 0, w!), sum(m=0, r\k, if(!m || !bittest(b, m), self()(r-k*m, k-1, bitor(b, 1<<m), w+m)/m!))))(n, n, 1, 0)} \\ Andrew Howroyd, Aug 31 2019
CROSSREFS
Row sums of A242887 and of A242896.
Cf. A098859 (the same for partitions).
Sequence in context: A262501 A225422 A290518 * A361426 A157285 A320068
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 25 2014
STATUS
approved