A191690
a(n) = n^n-n^(n-1)-n^(n-2)-...-n^2-n-1.
Original entry on oeis.org
0, 1, 14, 171, 2344, 37325, 686286, 14380471, 338992928, 8888888889, 256780503550, 8105545862051, 277635514376232, 10257237069745861, 406615755353655134, 17216961135462248175, 775537745518440716416, 37031913482632035365105
Offset: 1
a(1)=0 (=1^1-1), a(2)=1 (=2^2-2-1), a(3)=14 (=3^3-3^2-3-1), a(4)=171 (=4^4-4^3-4^2-4-1).
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A191690 := proc(n) n^n-add( n^j,j=0..n-1) ; end proc: # R. J. Mathar, Jun 23 2011
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Table[Total[-n^Range[0,n-1]]+n^n,{n,2,20}] (* Harvey P. Dale, Jul 06 2011 *)
f[n_] := ((n - 2) n^n + n)/(n - 1) - 1; f[1] = 0; Array[f, 18] (* Robert G. Wilson v, Apr 16 2015 *)
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a(n) = n^n - sum(k=0, n-1, n^k); \\ Michel Marcus, Apr 16 2015
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[n^n - sum([n^k for k in range(n)]) for n in range(1,19)] # Danny Rorabaugh, Apr 20 2015
A290844
Square array read by antidiagonals downwards: A(n, k) = (Sum_{i=1..n} i^k) - (n+1)^k for n >= 1, k >= 1.
Original entry on oeis.org
-1, -3, 0, -7, -4, 2, -15, -18, -2, 5, -31, -64, -28, 5, 9, -63, -210, -158, -25, 19, 14, -127, -664, -748, -271, 9, 42, 20, -255, -2058, -3302, -1825, -317, 98, 76, 27, -511, -6304, -14068, -10735, -3351, -126, 272, 123, 35, -1023, -19170, -58718, -59425, -26141, -4606, 580, 567, 185, 44
Offset: 1
Array starts
-1, -3, -7, -15, -31, -63, -127, -255
0, -4, -18, -64, -210, -664, -2058, -6304
2, -2, -28, -158, -748, -3302, -14068, -58718
5, 5, -25, -271, -1825, -10735, -59425, -318271
9, 19, 9, -317, -3351, -26141, -183111, -1216637
14, 42, 98, -126, -4606, -50478, -446782, -3622206
20, 76, 272, 580, -3760, -77324, -896848, -8869820
27, 123, 567, 2211, 2727, -84477, -1485513, -18362109
35, 185, 1025, 5333, 20825, -21595, -1919575, -32268667
44, 264, 1694, 10692, 59774, 206844, -1406746, -46627548
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x(n, k) = sum(i=1, n, i^k)
y(n, k) = (n+1)^k
a(n, k) = x(n, k) - y(n, k)
array(rows, cols) = for(s=1, rows, for(t=1, cols, print1(a(s, t), ", ")); print(""))
array(10, 8) \\ print initial 10 rows and 8 columns of array
A341331
a(n) = n^n - (n-1)^n - (n-2)^n - ... - 1^n.
Original entry on oeis.org
1, 3, 18, 158, 1825, 26141, 446782, 8869820, 200535993, 5085658075, 142947350986, 4410243535402, 148156328308105, 5382924338773177, 210309307208574750, 8791961076113491704, 391581231268402937041, 18510377905675629883959, 925555262359725659407258
Offset: 1
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f:= proc(n) local k; n^n - add(k^n,k=1..n-1) end proc:
map(f, [$1..30]); # Robert Israel, Feb 10 2021
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a[n_] := n^n - Sum[k^n, {k, 0, n - 1}]; Array[a, 20] (* Amiram Eldar, Apr 28 2021 *)
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a(n) = n^n-sum(k=0, n-1, k^n);
Showing 1-3 of 3 results.
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