A051128 Table T(n,k) = n^k read by upwards antidiagonals (n >= 1, k >= 1).
1, 2, 1, 3, 4, 1, 4, 9, 8, 1, 5, 16, 27, 16, 1, 6, 25, 64, 81, 32, 1, 7, 36, 125, 256, 243, 64, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1, 11, 100, 729, 4096, 16807, 46656, 78125, 65536, 19683, 1024, 1
Offset: 1
Examples
Table begins 1, 1, 1, 1, 1, ... 2, 4, 8, 16, 32, ... 3, 9, 27, 81, 243, ... 4, 16, 64, 256, 1024, ...
Links
- T. D. Noe, Rows n=1..50 of triangle, flattened
- G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], 2003.
Programs
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Maple
A051128 := proc(n) # Boris Putievskiy's formula a := floor((sqrt(8*n-7)+1)/2); b := (a+a^2)/2-n; c := (a-a^2)/2+n; (b+1)^c end: seq(A051128(n), n=1..61); # Peter Luschny, Dec 14 2012 # second Maple program: T:= (n, k)-> n^k: seq(seq(T(1+d-k, k), k=1..d), d=1..11); # Alois P. Heinz, Apr 18 2020
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Mathematica
Table[n^(k - n + 1), {k, 1, 11}, {n, k, 1, -1}] // Flatten (* Jean-François Alcover, Dec 14 2012 *) -
PARI
T(n,k) = n^k \\ Charles R Greathouse IV, Feb 09 2017
Formula
a(n) = A004736(n)^A002260(n) or ((t*t+3*t+4)/2-n)^(n-(t*(t+1)/2)), where t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 14 2012
Extensions
More terms from James Sellers, Dec 11 1999
Comments