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A336516
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Sum of parts, counted without multiplicity, in all compositions of n.
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5
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0, 1, 3, 10, 24, 59, 136, 309, 682, 1493, 3223, 6904, 14675, 31013, 65202, 136512, 284748, 592082, 1227709, 2539516, 5241640, 10798133, 22206568, 45597489, 93495667, 191464970, 391636718, 800233551, 1633530732, 3331568080, 6789078236, 13824212219, 28129459098
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(4) = 1 + 1 + 2 + 1 + 2 + 1 + 2 + 2 + 1 + 3 + 3 + 1 + 4 = 24: (1)111, (1)1(2), (1)(2)1, (2)(1)1, (2)2, (1)(3), (3)(1), (4).
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MAPLE
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b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
`if`(i<1, 0, add((p-> [0, `if`(j=0, 0, p[1]*i)]+p)(
b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..38);
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0},
If[i < 1, {0, 0}, Sum[Function[{0, If[j == 0, 0, #[[1]]*i]} + #][
b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
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CROSSREFS
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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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