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A004248 Table of x^y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),... 14

%I

%S 1,0,1,0,1,1,0,1,2,1,0,1,4,3,1,0,1,8,9,4,1,0,1,16,27,16,5,1,0,1,32,81,

%T 64,25,6,1,0,1,64,243,256,125,36,7,1,0,1,128,729,1024,625,216,49,8,1,

%U 0,1,256,2187,4096,3125,1296,343,64,9,1,0,1,512,6561,16384,15625,7776,2401,512,81,10,1

%N Table of x^y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...

%C As a number triangle, columns have g.f. x^k/(1-kx). Row sums are A026898, diagonal sums are A104872. - _Paul Barry_, Mar 28 2005

%H T. D. Noe, <a href="/A004248/b004248.txt">Rows n=0..50 of triangle, flattened</a>

%H Michelle Rudolph-Lilith, <a href="http://arxiv.org/abs/1508.07894">On the Product Representation of Number Sequences, with Application to the Fibonacci Family</a>, arXiv preprint arXiv:1508.07894 [math.NT], 2015.

%F Number triangle T(n, k)=if(k<=n, k^(n-k), 0); T(n, k)=sum{j=0..floor((n-k)/2), (-1)^j*C(n-k, j)C(n-k-j, n-k)k^(n-k-2j)}; - _Paul Barry_, Jul 13 2005

%e 1; 0,1; 0,1,1; 0,1,2,1; 0,1,4,3,1; ...

%t T[x_, y_] := If[y == 0, 1, (x - y)^y];

%t Table[T[x, y], {x, 0, 11}, {y, x, 0, -1}] // Flatten (* _Jean-Fran├žois Alcover_, Dec 15 2017 *)

%o (PARI) T(x,y)=x^y \\ _Charles R Greathouse IV_, Feb 07 2017

%Y Cf. A003992, A048723.

%Y For other versions see A051129 and A009998.

%K tabl,nonn,easy,nice

%O 0,9

%A _David W. Wilson_

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)