OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k, q) = c(n,q)/(c(k, q)*c(n-k, q)) where c(n, k) = Product_{j=1..n} (q*(2*q - 1))^j and q = 4.
From G. C. Greubel, Jun 30 2021: (Start)
T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 4.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 26.
T(n, k, p) = binomial(p+2, 2)^(k*(n-k)) with p = 6. (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 28, 1;
1, 784, 784, 1;
1, 21952, 614656, 21952, 1;
1, 614656, 481890304, 481890304, 614656, 1;
1, 17210368, 377801998336, 10578455953408, 377801998336, 17210368, 1;
MATHEMATICA
T[n_, k_, q_] = Binomial[2*q, 2]^(k*(n-k));
Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)
With[{m=26}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(Magma) [(28)^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[(28)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
Cf. A000384.
Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), A176642 (m=6), A158117 (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), this sequence (m=26).
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 22 2010
EXTENSIONS
Edited by G. C. Greubel, Jun 30 2021
STATUS
approved