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A278947
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Expansion of Sum_{k>=1} (k*(5*k - 3)/2)*x^k/(1 - x^k).
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2
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0, 1, 8, 19, 42, 56, 107, 113, 190, 208, 298, 287, 483, 404, 589, 614, 806, 698, 1079, 875, 1302, 1202, 1471, 1289, 2035, 1581, 2062, 1990, 2541, 2060, 3142, 2357, 3318, 2978, 3544, 3178, 4641, 3368, 4435, 4166, 5390, 4142, 6106, 4559, 6279, 5798, 6517, 5453, 8339, 6042, 7998, 7142, 8778, 6944, 10070, 7822, 10445, 8930, 10390
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OFFSET
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0,3
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COMMENTS
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Inverse Moebius transform of heptagonal numbers (A000566).
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
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FORMULA
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G.f.: Sum_{k>=1} (k*(5*k - 3)/2)*x^k/(1 - x^k).
Dirichlet g.f.: (5*zeta(s-2) - 3*zeta(s-1))*zeta(s)/2.
a(n) = Sum_{d|n} d*(5*d - 3)/2.
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MATHEMATICA
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nmax=58; CoefficientList[Series[Sum[(k (5 k - 3)/2) x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Flatten[{0, Table[(5*DivisorSigma[2, n] - 3*DivisorSigma[1, n])/2, {n, 1, 100}]}] (* Vaclav Kotesovec, Dec 05 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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