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A092265
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Sum of smallest parts of all partitions of n into distinct parts.
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10
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1, 2, 4, 5, 8, 10, 14, 16, 23, 26, 34, 40, 50, 58, 74, 83, 102, 120, 142, 164, 198, 226, 266, 308, 359, 412, 482, 548, 634, 730, 834, 950, 1094, 1240, 1416, 1609, 1826, 2068, 2350, 2648, 2994, 3382, 3806, 4280, 4826, 5408, 6070, 6806, 7619, 8522, 9534, 10632
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{n >= 1} (-1 + Product_k >= n} 1 + x^k).
G.f.: Sum_{n >= 1} n*x^n*Product_{k >= n+1} (1 + x^k). - Joerg Arndt, Jan 29 2011
G.f.: Sum_{k >= 1} x^(k*(k+1)/2)/(1 - x^k)/Product_{i = 1..k} (1 - x^i). - Vladeta Jovovic, Aug 10 2004
a(n) ~ exp(Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 20 2018
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, b(n, i+1)+b(n-i, i+1)))
end:
a:= n-> add(j*b(n-j, j+1), j=1..n):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]]]; a[n_] := Sum[j*b[n - j, j + 1], {j, 1, n}]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Jan 21 2017, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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STATUS
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approved
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