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A327238
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Expansion of Sum_{k>=1} ((1 + k * x^k)^k - 1).
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6
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1, 4, 9, 20, 25, 63, 49, 160, 108, 350, 121, 940, 169, 1225, 1475, 2304, 289, 7560, 361, 8025, 12446, 7139, 529, 58192, 3750, 13858, 61965, 102655, 841, 191181, 961, 318464, 220704, 40460, 354172, 1304370, 1369, 63175, 629863, 4012608, 1681, 1916733, 1849
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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) = Sum_{d|n} (n/d)^d * binomial(n/d,d).
a(p) = p^2, where p is prime.
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MATHEMATICA
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nmax = 43; CoefficientList[Series[Sum[((1 + k x^k)^k - 1), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (n/#)^# Binomial[n/#, #] &], {n, 1, 43}]
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PROG
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(PARI) a(n)={sumdiv(n, d, (n/d)^d * binomial(n/d, d))} \\ Andrew Howroyd, Sep 14 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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