A367011
a(n) = Sum_{k=0..n} k! * k^(n-k).
Original entry on oeis.org
1, 1, 3, 11, 51, 287, 1899, 14447, 124251, 1192127, 12623979, 146250287, 1840024251, 24983863967, 364140992139, 5670546353807, 93960923507931, 1650688221777407, 30646388716777899, 599565840087487727, 12328458398407260411
Offset: 0
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Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}]
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a(n) = sum(k=0, n, k!*k^(n-k)); \\ Seiichi Manyama, Dec 31 2023
A350149
Triangle read by rows: T(n, k) = n^(n-k)*k!.
Original entry on oeis.org
1, 1, 1, 4, 2, 2, 27, 9, 6, 6, 256, 64, 32, 24, 24, 3125, 625, 250, 150, 120, 120, 46656, 7776, 2592, 1296, 864, 720, 720, 823543, 117649, 33614, 14406, 8232, 5880, 5040, 5040, 16777216, 2097152, 524288, 196608, 98304, 61440, 46080, 40320, 40320
Offset: 0
Triangle T(n,k) begins:
--------------------------------------------------------------------------
n/k 0 1 2 3 4 5 6 7 8
--------------------------------------------------------------------------
0 | 1,
1 | 1, 1,
2 | 4, 2, 2,
3 | 27, 9, 6, 6,
4 | 256, 64, 32, 24, 24,
5 | 3125, 625, 250, 150, 120, 120,
6 | 46656, 7776, 2592, 1296, 864, 720, 720,
7 | 823543, 117649, 33614, 14406, 8232, 5880, 5040, 5040,
8 | 16777216, 2097152, 524288, 196608, 98304, 61440, 46080, 40320, 40320.
...
- Borwein, J., Bailey, D. and Girgensohn, R., Experimentation in Mathematics: Computational Paths to Discovery, A. K. Peters 2004.
- William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton NJ 2005.
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A350149:= func< n,k | n^(n-k)*Factorial(k) >;
[A350149(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 31 2022
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T := (n, k) -> n^(n - k)*k!:
seq(seq(T(n, k), k = 0..n), n = 0..9); # Peter Luschny, Jan 07 2022
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T[n_, k_]:= n^(n-k)*k!; Table[T[n, k], {n, 0,12}, {k,0,n}]//Flatten (* Amiram Eldar, Dec 27 2021 *)
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def A350149(n,k): return n^(n-k)*factorial(k)
flatten([[A350149(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 31 2022
A368561
a(n) = Sum_{k=0..n} k! * n^k.
Original entry on oeis.org
1, 2, 11, 184, 6565, 390806, 34557919, 4237440628, 687219772553, 142347286888210, 36654963132246211, 11483715014356017104, 4300711472638444724653, 1897241450053063830832078, 973695564434830963964311655
Offset: 0
A368555
a(n) = Sum_{k=0..n} k! * 3^(n-k).
Original entry on oeis.org
1, 4, 14, 48, 168, 624, 2592, 12816, 78768, 599184, 5426352, 56195856, 647589168, 8169788304, 111687656112, 1642737336336, 25851001897008, 433240433787024, 7702095007089072, 144751385430099216, 2867156164466937648, 59692410665110252944
Offset: 0
Showing 1-4 of 4 results.
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