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A176639
Triangle T(n, k) = 15^(k*(n-k)), read by rows.
14
1, 1, 1, 1, 15, 1, 1, 225, 225, 1, 1, 3375, 50625, 3375, 1, 1, 50625, 11390625, 11390625, 50625, 1, 1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1, 1, 11390625, 576650390625, 129746337890625, 129746337890625, 576650390625, 11390625, 1
OFFSET
0,5
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 = 3.
T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 3.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 13. - G. C. Greubel, Jun 30 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 15, 1;
1, 225, 225, 1;
1, 3375, 50625, 3375, 1;
1, 50625, 11390625, 11390625, 50625, 1;
1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1;
MATHEMATICA
(* First program *)
T[n_, k_, q_] = Binomial[2*q, 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=13}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(Magma) [(15)^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[(15)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
Cf. A000384.
Cf. A158116 (q=2), this sequence (q=3), A176641 (q=4).
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), this sequence (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26).
Sequence in context: A174693 A340430 A022178 * A015139 A040231 A040232
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 22 2010
EXTENSIONS
Edited by G. C. Greubel, Jun 30 2021
STATUS
approved