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%I #31 Feb 16 2022 09:42:21
%S 1,4,3,64,25,6,2401,512,81,10,161051,20736,2197,196,15,16777216,
%T 1419857,104976,6859,400,21,2494357888,148035889,7962624,390625,17576,
%U 729,28,500246412961,21870000000,887503681,33554432,1185921,39304,1225,36
%N Square array T(n,k) = ((n+k-1)*(n+k-2)/2+n)^k, n,k > 0 read by antidiagonals.
%C Column number k of the table T(n,k) is formula for Cantor antidiagonal order in power k
%H Boris Putievskiy, <a href="/A220556/b220556.txt">Table of n, Rows n = 1 to 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^A004763 or a(n) = n^((t*t+3*t+4)/2 - n), where t=floor((-1+sqrt(8*n-7))/2).
%e Square array T(n,k) begins:
%e 1, 4, 64, 2401, 161051, ...
%e 3, 25, 512, 20736, 1419857, ...
%e 6, 81, 2197, 104976, 7962624, ...
%e 10, 196, 6859, 390625, 33554432, ...
%e 15, 400, 17576, 1185921, 115856201, ...
%e 21, 729, 39304, 3111696, 345025251, ...
%e ...
%e The start of the sequence as triangle array is:
%e 1;
%e 4, 3;
%e 64, 25, 6;
%e 2401, 512, 91, 10;
%e 161051, 20736, 2197, 196, 15;
%e ...
%o (Python)
%o t=int((math.sqrt(8*n-7) - 1)/ 2)
%o m=n**((t*t+3*t+4)/2-n)
%Y Column k=1 gives: A000217.
%Y Cf. A004736.
%K nonn,tabl
%O 1,2
%A _Boris Putievskiy_, Dec 16 2012
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