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 A242882 Number of compositions of n into parts with distinct multiplicities. 29
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..264 (terms 0..200 from Alois P. Heinz) Vaclav Kotesovec, What is the limit a(n)/2^n ? 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<

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Last modified June 4 17:14 EDT 2020. Contains 334828 sequences. (Running on oeis4.)