A352982
a(n) = Sum_{k=0..floor(n/3)} k^n.
Original entry on oeis.org
1, 0, 0, 1, 1, 1, 65, 129, 257, 20196, 60074, 179196, 17312754, 68711380, 273234810, 31605701625, 156925970179, 780248593545, 105443761093411, 628709267031321, 3752628871164355, 580964060390826448, 4043844561787569140, 28170468954985342384
Offset: 0
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[(&+[k^n: k in [0..Floor(n/3)]]): n in [0..40]]; // G. C. Greubel, Nov 01 2022
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a[0] = 1; a[n_] := Sum[k^n, {k, 0, Floor[n/3]}]; Array[a, 24, 0] (* Amiram Eldar, Apr 13 2022 *)
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a(n) = sum(k=0, n\3, k^n);
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my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^(3*k)/(1-k*x)))
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[sum( k^n for k in range((n//3)+1)) for n in range(41)] # G. C. Greubel, Nov 01 2022
A355575
a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/k!.
Original entry on oeis.org
1, 0, 0, 6, 24, 120, 1080, 10080, 120960, 1874880, 34473600, 738460800, 17982518400, 489858969600, 14834839219200, 498452777222400, 18583796335104000, 768773914900992000, 35220800475250790400, 1779227869201400217600, 98469904378626772992000
Offset: 0
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Join[{1}, Table[n!*Sum[k^(n - 3*k)/k!, {k, 0, n/3}], {n, 1, 20}]] (* Vaclav Kotesovec, Oct 30 2022 *)
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a(n) = n!*sum(k=0, n\3, k^(n-3*k)/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^(3*k)/(k!*(1-k*x)))))
A352986
a(n) = Sum_{k=0..floor(n/3)} k^(3*(n-3*k)).
Original entry on oeis.org
1, 0, 0, 1, 1, 1, 2, 9, 65, 514, 4124, 33498, 281829, 2628658, 31130220, 521900363, 11550872369, 292093228523, 7763038391586, 210839178560483, 5844964107402065, 168148032885913260, 5206234971937519704, 183267822341124743772, 7684147885975909244473
Offset: 0
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a[0] = 1; a[n_] := Sum[k^(3*(n - 3*k)), {k, 0, Floor[n/3]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 13 2022 *)
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a(n) = sum(k=0, n\3, k^(3*(n-3*k)));
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my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/(1-k^3*x)))
Showing 1-3 of 3 results.