A168658
a(n) = ceiling(n^n/2).
Original entry on oeis.org
1, 1, 2, 14, 128, 1563, 23328, 411772, 8388608, 193710245, 5000000000, 142655835306, 4458050224128, 151437553296127, 5556003412779008, 218946945190429688, 9223372036854775808, 413620130943168382089
Offset: 0
Cf.
A000312 (all endofunctions of degree n)
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[Ceiling(n^n/2): n in [0..20]]; // Vincenzo Librandi, Aug 29 2011
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Join[{1}, Table[Ceiling[n^n/2], {n, 1, 25}]] (* G. C. Greubel, Jul 28 2016 *)
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a(n) = ceil(n^n/2); \\ Michel Marcus, Feb 18 2016
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[ceil(n^n/2) for n in range(0,21)]#
A057075
Table read by antidiagonals of T(n,k)=floor(n^n/k) with n,k >= 1.
Original entry on oeis.org
1, 0, 4, 0, 2, 27, 0, 1, 13, 256, 0, 1, 9, 128, 3125, 0, 0, 6, 85, 1562, 46656, 0, 0, 5, 64, 1041, 23328, 823543, 0, 0, 4, 51, 781, 15552, 411771, 16777216, 0, 0, 3, 42, 625, 11664, 274514, 8388608, 387420489, 0, 0, 3, 36, 520, 9331, 205885, 5592405, 193710244, 10000000000
Offset: 1
From _Seiichi Manyama_, Aug 12 2023: (Start)
Square array begins:
1, 0, 0, 0, 0, 0, ...
4, 2, 1, 1, 0, 0, ...
27, 13, 9, 6, 5, 4, ...
256, 128, 85, 64, 51, 42, ...
3125, 1562, 1041, 781, 625, 520, ...
46656, 23328, 15552, 11664, 9331, 7776, ... (End)
A369072
Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).
Original entry on oeis.org
0, 0, 0, 0, 2, 2, 0, 13, 9, 18, 0, 128, 72, 96, 216, 0, 1562, 800, 900, 1350, 3200, 0, 23328, 11250, 11520, 14580, 23040, 56250, 0, 411771, 190512, 183750, 211680, 282240, 459375, 1143072, 0, 8388608, 3764768, 3483648, 3780000, 4587520, 6300000, 10450944, 26353376
Offset: 0
Triangle starts:
[0] [0]
[1] [0, 0]
[2] [0, 2, 2]
[3] [0, 13, 9, 18]
[4] [0, 128, 72, 96, 216]
[5] [0, 1562, 800, 900, 1350, 3200]
[6] [0, 23328, 11250, 11520, 14580, 23040, 56250]
[7] [0, 411771, 190512, 183750, 211680, 282240, 459375, 1143072]
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A369072[n_, k_] := Floor[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] n (n-k+1)^(n-k) / 2];
Table[A369072[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 13 2024 *)
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def A369072(n, k):
return binomial(n, k-1)*(k-1)^(k-1)*n*(n-k+1)^(n-k)//2
for n in range(9): print([A369072(n, k) for k in range(n+1)])
A068595
Number of functions from {1,2,...,n} to {1,2,...,n} such that the sum of the function values is 0 mod 3.
Original entry on oeis.org
0, 2, 9, 85, 1041, 15552, 274514, 5592406, 129140163, 3333333333, 95103890203, 2972033482752, 100958368864084, 3704002275186006, 145964630126953125, 6148914691236517205, 275746753962112254725, 13115469358432179191808, 659473218553437863041326, 34952533333333333333333334
Offset: 1
Showing 1-4 of 4 results.
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