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A242391
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Number of compositions of n in which each part has odd multiplicity.
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3
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1, 1, 1, 4, 3, 10, 16, 28, 49, 91, 186, 266, 670, 884, 2350, 3028, 8259, 10536, 30241, 37382, 108628, 135550, 391202, 503750, 1429838, 1884659, 5222976, 7107138, 19119324, 27088726, 70366026, 103884570, 259884905, 399686188, 962312254, 1543116240, 3576132805
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OFFSET
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0,4
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LINKS
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EXAMPLE
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a(0) = 1: the empty composition.
a(1) = 1: [1].
a(2) = 1: [2].
a(3) = 4: [3], [2,1], [1,2], [1,1,1].
a(4) = 3: [4], [3,1], [1,3].
a(5) = 10: [5], [4,1], [1,4], [3,2], [2,3], [2,1,1,1], [1,2,1,1], [1,1,2,1], [1,1,1,2], [1,1,1,1,1].
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MAPLE
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b:= proc(n, i, p) option remember; `if`(n=0, p!,
`if`(i<1, 0, add(`if`(j=0 or irem(j, 2)=1,
b(n-i*j, i-1, p+j)/j!, 0), j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..45);
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, Sum[If[j==0 || Mod[j, 2]==1, b[n-i*j, i-1, p+j]/j!, 0], {j, 0, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Feb 08 2017, translated from Maple *)
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CROSSREFS
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Cf. A130495 (for even multiplicity).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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