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A280025
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Expansion of phi_{7, 4}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
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2
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0, 1, 144, 2268, 18688, 78750, 326592, 825944, 2396160, 4966677, 11340000, 19501812, 42384384, 62777078, 118935936, 178605000, 306774016, 410422194, 715201488, 894002060, 1471680000, 1873240992, 2808260928, 3405105288, 5434490880, 6152734375, 9039899232
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^8, where c = Pi^4/720 = 0.1352904... (= A152649 / 10). - Amiram Eldar, Dec 08 2022
Multiplicative with a(p^e) = p^(4*e) * (p^(3*e+3)-1)/(p^3-1).
Dirichlet g.f.: zeta(s-4)*zeta(s-7). (End)
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MATHEMATICA
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Table[n^4 * DivisorSigma[3, n], {n, 0, 30}] (* Amiram Eldar, Oct 31 2023 *)
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PROG
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(PARI) a(n) = if(n < 1, 0, n^4 * sigma(n, 3)); \\ Andrew Howroyd, Jul 23 2018
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CROSSREFS
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Cf. A280022 (phi_{5, 4}), this sequence (phi_{7, 4}).
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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