A176639 - OEIS

%I #12 Sep 08 2022 08:45:53

%S 1,1,1,1,15,1,1,225,225,1,1,3375,50625,3375,1,1,50625,11390625,

%T 11390625,50625,1,1,759375,2562890625,38443359375,2562890625,759375,1,

%U 1,11390625,576650390625,129746337890625,129746337890625,576650390625,11390625,1

%N Triangle T(n, k) = 15^(k*(n-k)), read by rows.

%H G. C. Greubel, <a href="/A176639/b176639.txt">Rows n = 0..50 of the triangle, flattened</a>

%F 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.

%F T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 3.

%F T(n, k, m) = (m+2)^(k*(n-k)) with m = 13. - _G. C. Greubel_, Jun 30 2021

%e Triangle begins as:

%e   1;

%e   1,      1;

%e   1,     15,          1;

%e   1,    225,        225,           1;

%e   1,   3375,      50625,        3375,          1;

%e   1,  50625,   11390625,    11390625,      50625,      1;

%e   1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1;

%t (* First program *)

%t T[n_, k_, q_] = Binomial[2*q, 2]^(k*(n-k));

%t Table[T[n, k, 3], {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jun 30 2021 *)

%t (* Second program *)

%t With[{m=13}, Table[(m+2)^(k*(n-k)), {n,0,12}, {k,0,n}]//Flatten] (* _G. C. Greubel_, Jun 30 2021 *)

%o (Magma) [(15)^(k*(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 30 2021

%o (Sage) flatten([[(15)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 30 2021

%Y Cf. A000384.

%Y Cf. A158116 (q=2), this sequence (q=3), A176641 (q=4).

%Y 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).

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Apr 22 2010

%E Edited by _G. C. Greubel_, Jun 30 2021