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A004248 Table of x^y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),... 13
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, 64, 25, 6, 1, 0, 1, 64, 243, 256, 125, 36, 7, 1, 0, 1, 128, 729, 1024, 625, 216, 49, 8, 1, 0, 1, 256, 2187, 4096, 3125, 1296, 343, 64, 9, 1, 0, 1, 512, 6561, 16384, 15625, 7776, 2401, 512, 81, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

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

LINKS

T. D. Noe, Rows n=0..50 of triangle, flattened

Michelle Rudolph-Lilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894 [math.NT], 2015.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

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

PROG

(PARI) T(x, y)=x^y \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A003992, A048723.

For other versions see A051129 and A009998.

Sequence in context: A119328 A048723 A088455 * A034373 A238889 A296207

Adjacent sequences:  A004245 A004246 A004247 * A004249 A004250 A004251

KEYWORD

tabl,nonn,easy,nice

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 15 13:59 EST 2018. Contains 318149 sequences. (Running on oeis4.)