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A336771
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Total sum of the left-to-right maxima in all compositions of n into distinct parts.
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4
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0, 1, 2, 8, 11, 22, 53, 75, 123, 193, 418, 538, 894, 1268, 1950, 3567, 4799, 7143, 10355, 14968, 20701, 36398, 46420, 69071, 94972, 136385, 182522, 259104, 402405, 527090, 741569, 1015491, 1397661, 1880541, 2567202, 3392612, 5153156, 6553844, 9088372, 12040797
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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(6) = 53 = 6+4+5+5+3+3+6+4+6+5+6: (1)(2)(3), (1)(3)2, (2)1(3), (2)(3)1, (3)12, (3)21, (2)(4), (4)2, (1)(5), (5)1, (6).
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MAPLE
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b:= proc(n, i, k, m) option remember; `if`(i<k or n>
(2*i-k+1)*k/2, 0, `if`(n=0, [1, 0], b(n, i-1, k, m)+
(p-> p+[0, p[1]*i/(m+1-k)])(b(n-i, min(n-i, i-1), k-1, m))))
end:
a:= n-> add(b(n$2, k$2)[2]*k!, k=1..floor((sqrt(8*n+1)-1)/2)):
seq(a(n), n=0..40);
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MATHEMATICA
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b[n_, i_, k_, m_] := b[n, i, k, m] = If[i < k || n >
(2*i - k + 1)*k/2, {0, 0}, If[n == 0, {1, 0}, b[n, i - 1, k, m] +
Function[p, p+{0, p[[1]]*i/(m+1-k)}][b[n-i, Min[n-i, i-1], k-1, m]]]];
a[n_] := Sum[b[n, n, k, k][[2]]*k!, {k, 1, Floor[(Sqrt[8*n + 1] - 1)/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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