OFFSET
0,4
COMMENTS
Triangle T(n,k), 0 <= k <= n, read by rows given by [1, q-1, q^2, q^3-q, q^4, q^5-q^2, q^6, q^7-q^3, q^8, ...] DELTA [-1, 0, -q, 0, -q^2, 0, -q^3, 0, -q^4, 0, ...] (for q=-2) = [1, -3, 4, -6, 16, -36, 64,...] DELTA [ -1, 0, 2, 0, -4, 0, 8, 0, -16, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 10 2009
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
Sum_{k=0..n} T(n, k) = 0^n.
From G. C. Greubel, Nov 29 2021: (Start)
T(n, k) = [x^k] coefficients of the polynomials defined by q^binomial(n, 2)*QPochhammer(x, 1/q, n), where q = -2.
T(n, k) = [x^k] Product_{j=0..n-1} (q^j - x). (End)
EXAMPLE
Triangle begins as:
1;
1, -1;
-2, 1, 1;
-8, 6, 3, -1;
64, -40, -30, 5, 1;
1024, -704, -440, 110, 11, -1;
-32768, 21504, 14784, -3080, -462, 21, 1;
-2097152, 1409024, 924672, -211904, -26488, 1806, 43, -1;
268435456, -178257920, -119767040, 26199040, 3602368, -204680, -7310, 85, 1;
MATHEMATICA
p[x_, n_, q_]:= q^Binomial[n, 2]*QPochhammer[x, 1/q, n];
Table[CoefficientList[Series[p[x, n, -2], {x, 0, n}], x], {n, 0, 10}]//Flatten (* G. C. Greubel, Nov 29 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Mar 06 2009
EXTENSIONS
Edited by G. C. Greubel, Nov 29 2021
STATUS
approved