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A360770
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Expansion of Sum_{k>0} (x * (k + x^k))^k.
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0
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1, 5, 27, 260, 3125, 46684, 823543, 16777472, 387420498, 10000003125, 285311670611, 8916100495009, 302875106592253, 11112006826381559, 437893890380860625, 18446744073726328848, 827240261886336764177, 39346408075296925015353
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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} d^(d-n/d+1) * binomial(d,n/d-1).
If p is an odd prime, a(p) = p^p.
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(# - n/# + 1) * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (x*(k+x^k))^k))
(PARI) a(n) = sumdiv(n, d, d^(d-n/d+1)*binomial(d, n/d-1));
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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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