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Table T(n,k) = ((n+k-1)*(n+k-2)/2+n)^n, n,k >0 read by antidiagonals.
3

%I #38 Feb 16 2022 18:24:51

%S 1,2,9,4,25,216,7,64,729,10000,11,144,2197,38416,759375,16,289,5832,

%T 130321,3200000,85766121,22,529,13824,390625,11881376,387420489,

%U 13492928512,29,900,29791,1048576,39135393,1544804416,64339296875,2821109907456

%N Table T(n,k) = ((n+k-1)*(n+k-2)/2+n)^n, n,k >0 read by antidiagonals.

%C The first column is A000124.

%H Boris Putievskiy, <a href="/A220416/b220416.txt">Rows n = 1..30 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.

%F As a linear array, the sequence is a(n) = n^A002260(n) or

%F a(n) = n^(n-t(t+1)/2), where t=floor[(-1+sqrt(8*n-7))/2].

%e The start of the sequence as triangle array is:

%e 1;

%e 2,9;

%e 4,25,216;

%e 7,64,729,10000;

%e 11, 144, 2197, 38416, 759375;

%e ...

%o (Python)

%o t=int((math.sqrt(8*n-7) - 1)/ 2)

%o m=n**(n-t*(t+1)/2)

%Y Cf. A002260, A000124.

%K nonn,tabl

%O 1,2

%A _Boris Putievskiy_, Dec 14 2012