A353013
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-k).
Original entry on oeis.org
1, 1, 4, 28, 264, 3207, 47696, 839412, 17061280, 393264145, 10135913792, 288839201432, 9017184333440, 306045200463519, 11220008681600256, 441866073895351128, 18603606156815235584, 833860238440653331505, 39643749441387211150336
Offset: 0
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a[0] = 1; a[n_] := Sum[(n - 2*k)^(n - k), {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)
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a(n) = sum(k=0, n\2, (n-2*k)^(n-k));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k*x^2)))
A353015
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n.
Original entry on oeis.org
1, 1, 4, 27, 257, 3157, 47385, 839928, 17168097, 397517868, 10283523826, 293950435376, 9200707298514, 312972062711525, 11496160809184370, 453507273286873875, 19122193920118268355, 858239308206920523297, 40851073484808464297979
Offset: 0
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a[0] = 1; a[n_] := Sum[(n-3*k)^n, {k, 0, Floor[n/3]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)
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a(n) = sum(k=0, n\3, (n-3*k)^n);
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-(k*x)^3)))
A359700
a(n) = Sum_{d|n} d^(d + n/d - 1).
Original entry on oeis.org
1, 5, 28, 265, 3126, 46754, 823544, 16778273, 387420733, 10000015690, 285311670612, 8916100733146, 302875106592254, 11112006831323074, 437893890380939688, 18446744073843786241, 827240261886336764178, 39346408075300026047027
Offset: 1
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a[n_] := DivisorSum[n, #^(# + n/# - 1) &]; Array[a, 20] (* Amiram Eldar, Aug 14 2023 *)
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a(n) = sumdiv(n, d, d^(d+n/d-1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k*x^k)))
A353018
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-3*k).
Original entry on oeis.org
1, 1, 4, 28, 257, 3129, 46684, 823800, 16780345, 387467173, 10000823800, 285328450956, 8916487915429, 302885107416053, 11112292154008972, 437902806868774804, 18447046958816967669, 827251374178490773149, 39346845978103406350228
Offset: 0
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a[n_] := Sum[If[3*k == n, 1, (n - 3*k)^(n - 3*k)], {k, 0, Floor[n/3]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)
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a(n) = sum(k=0, n\3, (n-3*k)^(n-3*k));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k)/(1-x^3))
Showing 1-4 of 4 results.