OFFSET
1,4
LINKS
Boris Putievskiy, Rows n = 1..76 of triangle, flattened
FORMULA
EXAMPLE
The table T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
0 1 2 3 4 5 ...
-1 0 1 0 -7 -28 ...
-2 -1 0 -17 -118 -513 ...
-3 0 17 0 -399 -2800 ...
-4 7 118 399 0 -7849 ...
-5 28 513 2800 7849 0 ...
...
The start of the sequence as a triangular array, read by rows (i.e., descending antidiagonals of T(n,k)), is as follows:
0;
1, -1;
2, 0, -2;
3, 1, -1, -3;
4, 0, 0, 0, -4;
5, -7, -17, 17, 7, -5;
6, -28, -118, 0, 118, 28, -6;
...
In the above triangle, row number m contains m numbers: m^1 - 1^m, (m-1)^2 - 2^(m-1), ..., 1^m - m^1.
PROG
(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
m=((t*t+3*t+4)/2-n)**(n-t*(t+1)/2)-(n-t*(t+1)/2)**((t*t+3*t+4)/2-n)
(PARI) matrix(9, 9, n, k, k^n - n^k) \\ Michel Marcus, Oct 04 2019
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Boris Putievskiy, Dec 14 2012
STATUS
approved