A062810
a(n) = Sum_{i=1..n} i^(n - i) + (n - i)^i.
Original entry on oeis.org
1, 3, 7, 17, 45, 131, 419, 1465, 5561, 22755, 99727, 465537, 2303829, 12037571, 66174411, 381560425, 2301307841, 14483421859, 94909491607, 646309392369, 4565559980989, 33401808977411, 252713264780595, 1974606909857945
Offset: 1
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Sum[i^(n - i) + (n - i)^i, {i, 1, n}]
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a(n) = sum(i=1, n, i^(n-i) + (n-i)^i); \\ Michel Marcus, Mar 24 2019
A062812
a(n) = Sum_{i=1..n} i^(n - i) + (-1)^(n - i)*(n - i)^i.
Original entry on oeis.org
1, 1, 5, 9, 25, 65, 205, 713, 2753, 11425, 50389, 234825, 1155817, 6009153, 32958173, 190115849, 1148816017, 7244099617, 47521750501, 323632894729, 2284774880441, 16702573959489, 126299702576365, 986688266888777
Offset: 1
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Sum[i^(n - i) + (-1)^(n - i)*(n - i)^i, {i, 1, n}]
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a(n) = sum(i=1, n, i^(n-i) + (-1)^(n-i)*(n-i)^i); \\ Michel Marcus, Mar 24 2019
A353016
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).
Original entry on oeis.org
1, 1, 1, 2, 5, 11, 33, 108, 357, 1405, 5713, 24670, 117413, 574007, 3004577, 16608120, 95057925, 576245913, 3622049809, 23693870554, 161816447365, 1140392550275, 8351286979745, 63206781102116, 493344133444389, 3980464191557205, 33029872125113937, 282290255465835382
Offset: 0
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a[0] = 1; a[n_] := Sum[(n-2*k)^(2*k), {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *)
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a(n) = sum(k=0, n\2, (n-2*k)^(2*k));
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my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)))
Showing 1-3 of 3 results.