A353014
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-2*k).
Original entry on oeis.org
1, 1, 4, 27, 257, 3133, 46737, 824568, 16792857, 387700668, 10005768898, 285445966496, 8919588913002, 302975146962245, 11115146328067250, 438000914977377939, 18450682450377791691, 827395864513198608177, 39352977767853205024131
Offset: 0
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a[0] = 1; a[n_] := Sum[(n - 3*k)^(n - 2*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-2*k));
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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)))
A352082
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^n.
Original entry on oeis.org
1, 1, 4, 28, 272, 3369, 50816, 903856, 18522624, 429746905, 11135257600, 318719062236, 9987013488640, 340037795872369, 12500401969233920, 493467700789897408, 20819865970795610112, 934939160745193002321, 44523294861684890664960
Offset: 0
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a[0] = 1; a[n_] := Sum[(n-2*k)^n, {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);
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-(k*x)^2)))
A353009
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-2*k).
Original entry on oeis.org
1, 1, 5, 28, 261, 3153, 46917, 826696, 16824133, 388247185, 10016824133, 285699917796, 8926117272389, 303160806510049, 11120932942830405, 438197051187369424, 18457865006652382021, 827678458937524133601, 39364865940303189957445
Offset: 0
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a[n_] := Sum[If[2*k == n, 1, (n - 2*k)^(n - 2*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-2*k));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k)/(1-x^2))
Showing 1-4 of 4 results.