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) = binomial(q+2, 2)^binomial(n+1, 2), c(n, 0) = n!, and q = 3.
T(n, k, q) = binomial(q+2, 2)^(k*(n-k)) with q = 3.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 8. - G. C. Greubel, Jun 30 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 10, 1;
1, 100, 100, 1;
1, 1000, 10000, 1000, 1;
1, 10000, 1000000, 1000000, 10000, 1;
1, 100000, 100000000, 1000000000, 100000000, 100000, 1;
1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1;
MATHEMATICA
(* First program *)
T[n_, k_, q_]= Binomial[q+2, 2](k*(n-k));
Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)
(* Second program *)
With[{m=8}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(Magma) [10^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[10^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
Cf. A007318 (q=0), A118180 (q=1), A158116 (q=2), this sequence (q=3), A176639 (q=4), A176643 (q=5), A176641 (q=6).
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 12 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 30 2021
STATUS
approved