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)))
A353017
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(3*k).
Original entry on oeis.org
1, 1, 1, 1, 2, 9, 28, 66, 190, 946, 4441, 16650, 67069, 380795, 2220697, 11142307, 58133022, 380165427, 2581541092, 15919859932, 101602799146, 758173118356, 5826902270129, 42158185020684, 316416126945385, 2656178496077301, 22725296418141937, 187568834724460765
Offset: 0
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a[0] = 1; a[n_] := Sum[(n-3*k)^(3*k), {k, 0, Floor[n/3]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *)
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a(n) = sum(k=0, n\3, (n-3*k)^(3*k));
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my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^3)))
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))
A357174
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^n/(n - 3*k)!.
Original entry on oeis.org
1, 1, 4, 27, 280, 5045, 134136, 4269223, 153188176, 6657007113, 371930499280, 25072409219891, 1872319689314856, 154583203638018493, 14784597239881491400, 1641532369038107170815, 201617558936011146124576, 26755058016106471234608017
Offset: 0
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a[n_] := n! * Sum[(n - 3*k)^n/(n - 3*k)!, {k, 0, Floor[n/3]} ]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Sep 16 2022 *)
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a(n) = n!*sum(k=0, n\3, (n-3*k)^n/(n-3*k)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^k/(k!*(1-(k*x)^3)))))
Showing 1-4 of 4 results.