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A160399
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a(n) = sum{k=1 to n} binomial(n,k) * d(k), where d(k) = the number of positive divisors of k.
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1
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1, 4, 11, 27, 62, 137, 296, 630, 1326, 2768, 5744, 11867, 24429, 50135, 102627, 209641, 427518, 870579, 1770536, 3596614, 7298397, 14796658, 29974913, 60681233, 122767148, 248232863, 501648844, 1013257334, 2045684971
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2009: (Start)
Binomial transform of the sequence d(n) (A000005).
(End)
Apparently the partial sums of A101509. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2009]
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FORMULA
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2009: (Start)
G.f.=Sum([x/(1-x)]^k/[1-x^k/(1-x)^k],k=1..infinity)/(1-x).
(End)
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MAPLE
| with(numtheory): seq(sum(binomial(n, k)*tau(k), k = 1 .. n), n = 1 .. 30); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2009]
A160399 := proc(n) local k; add(binomial(n, k)*numtheory[tau](k), k=1..n) ; end: seq(A160399(n), n=1..40) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2009]
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CROSSREFS
| Cf. A000005 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2009]
Sequence in context: A014630 A192965 A035593 * A119706 A034345 A036890
Adjacent sequences: A160396 A160397 A160398 * A160400 A160401 A160402
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, May 12 2009
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2009
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