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A308812
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a(n) = Sum_{k=1..n} binomial(n,k) * floor(n/k).
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3
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1, 5, 13, 33, 61, 143, 246, 521, 985, 1995, 3499, 7923, 14028, 28642, 55603, 115369, 210665, 455399, 838338, 1755983, 3383652, 6974159, 13034492, 28011611, 52475486, 108821068, 210050941, 436273458, 824191369, 1744975533, 3301974301, 6867107913, 13250454241
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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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a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} binomial(n,k) * x^k/(1 - x^k).
a(n) = Sum_{k=1..n} Sum_{d|k} binomial(n,d).
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MAPLE
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f:= proc(n) local k; add(binomial(n, k)*floor(n/k), k=1..n) end proc:
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MATHEMATICA
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Table[Sum[Binomial[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 33}]
Table[SeriesCoefficient[1/(1 - x) Sum[Binomial[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 33}]
Table[Sum[Sum[Binomial[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 33}]
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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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