A338661
a(n) = Sum_{d|n} d^n * binomial(d+n/d-2, d-1).
Original entry on oeis.org
1, 5, 28, 289, 3126, 49036, 823544, 17040385, 387538588, 10048833246, 285311670612, 8929334253419, 302875106592254, 11116754387182648, 437894348359764856, 18448995959423107073, 827240261886336764178, 39347761059781438793815, 1978419655660313589123980
Offset: 1
-
a[n_] := DivisorSum[n, #^n * Binomial[# + n/# - 2, #-1] &]; Array[a, 20] (* Amiram Eldar, Apr 22 2021 *)
-
a(n) = sumdiv(n, d, d^n*binomial(d+n/d-2, d-1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-(k*x)^k))^k))
A343573
a(n) = Sum_{d|n} d^d * binomial(d+n/d-2, d-1).
Original entry on oeis.org
1, 5, 28, 265, 3126, 46750, 823544, 16778257, 387420652, 10000015646, 285311670612, 8916100731047, 302875106592254, 11112006831322846, 437893890380906656, 18446744073843774497, 827240261886336764178, 39346408075300025340205
Offset: 1
Cf.
A023887,
A157019,
A157020,
A324158,
A324159,
A338661,
A339481,
A339482,
A339712,
A343567,
A343574.
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a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 20 2021 *)
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a(n) = sumdiv(n, d, d^d*binomial(d+n/d-2, d-1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-x^k))^k))
A339481
a(n) = Sum_{d|n} d^(n-d) * binomial(d+n/d-2, d-1).
Original entry on oeis.org
1, 2, 2, 10, 2, 131, 2, 1282, 4376, 16907, 2, 1138272, 2, 5793475, 154455992, 469893122, 2, 49501130330, 2, 1318441711177, 19001093813466, 3138439911059, 2, 15989399214596398, 6675720214843752, 3937376603803099, 6754271297694102092, 47097064577536888014, 2
Offset: 1
-
a[n_] := DivisorSum[n, #^(n - #) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)
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a(n) = sumdiv(n, d, d^(n-d)*binomial(d+n/d-2, d-1));
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my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-(k*x)^k))^k))
A339712
a(n) = Sum_{d|n} d^(d+n/d-1) * binomial(d+n/d-2, d-1).
Original entry on oeis.org
1, 5, 28, 273, 3126, 46948, 823544, 16781441, 387421948, 10000078446, 285311670612, 8916102176891, 302875106592254, 11112006865913416, 437893890382064056, 18446744074783625217, 827240261886336764178, 39346408075327954053967, 1978419655660313589123980
Offset: 1
-
a[n_] := DivisorSum[n, #^(# + n/# - 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)
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a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d+n/d-2, d-1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-k*x^k))^k))
Showing 1-4 of 4 results.