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 *)
-
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))
A339482
a(n) = Sum_{d|n} d^(n-d+1) * binomial(d+n/d-2, d-1).
Original entry on oeis.org
1, 3, 4, 21, 6, 346, 8, 4617, 13132, 80696, 12, 4903847, 14, 40410966, 756336736, 2416181265, 18, 306560794753, 20, 6941876836216, 132964265599502, 34522735212626, 24, 116720277621236637, 33378601074218776, 51185893450298400, 60788365423272068968
Offset: 1
-
a[n_] := DivisorSum[n, #^(n - # + 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)
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a(n) = sumdiv(n, d, d^(n-d+1)*binomial(d+n/d-2, d-1));
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my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*(x/(1-(k*x)^k))^k))
A360824
Expansion of Sum_{k>0} (k * x)^k / (1 - k * x^k)^(k+1).
Original entry on oeis.org
1, 6, 30, 284, 3130, 47082, 823550, 16782664, 387422928, 10000094720, 285311670622, 8916102486528, 302875106592266, 11112006871683606, 437893890382576560, 18446744074918103056, 827240261886336764194, 39346408075331452862196
Offset: 1
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a[n_] := DivisorSum[n, #^(# + n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k*x^k)^(k+1)))
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a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d+n/d-1, d));
Showing 1-5 of 5 results.