OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n,k) = 6^(k*(n-k)). - Tom Edgar, Feb 20 2014
T(n,k) = (1/n)*(6^(n-k)*k*T(n-1,k-1) + 6^k*(n-k)*T(n-1,k)). - Tom Edgar, Feb 20 2014
From G. C. Greubel, Jun 30 2021: (Start)
T(n, k, m) = (m+2)^(k*(n-k)) with m = 4.
T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 2. (End)
EXAMPLE
Triangle starts:
1;
1, 1;
1, 6, 1;
1, 36, 36, 1;
1, 216, 1296, 216, 1;
1, 1296, 46656, 46656, 1296, 1;
1, 7776, 1679616, 10077696, 1679616, 7776, 1;
1, 46656, 60466176, 2176782336, 2176782336, 60466176, 46656, 1;
MATHEMATICA
With[{m=4}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(PARI) T(n, k) = 6^(k*(n-k));
for (n=0, 11, for (k=0, n, print1(T(n, k), ", ")); print(); ); \\ Joerg Arndt, Feb 21 2014
(Magma) [6^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[6^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 12 2009
EXTENSIONS
Overall edit and new name by Tom Edgar and Joerg Arndt, Feb 21 2014
STATUS
approved