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%I #13 Sep 08 2022 08:45:53
%S 1,1,1,1,12,1,1,144,144,1,1,1728,20736,1728,1,1,20736,2985984,2985984,
%T 20736,1,1,248832,429981696,5159780352,429981696,248832,1,1,2985984,
%U 61917364224,8916100448256,8916100448256,61917364224,2985984,1
%N Triangle T(n, k) = 12^(k*(n-k)), read by rows.
%H G. C. Greubel, <a href="/A176627/b176627.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*(3*q - 1)/2)^j and q = 3.
%F T(n, k, q) = (binomial(3*q, 2)/3)^(k*(n-k)) with q = 3.
%F T(n, k, m) = (m+2)^(k*(n-k)) with m = 10. - _G. C. Greubel_, Jun 30 2021
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 12, 1;
%e 1, 144, 144, 1;
%e 1, 1728, 20736, 1728, 1;
%e 1, 20736, 2985984, 2985984, 20736, 1;
%e 1, 248832, 429981696, 5159780352, 429981696, 248832, 1;
%e 1, 2985984, 61917364224, 8916100448256, 8916100448256, 61917364224, 2985984, 1;
%t (* First program *)
%t T[n_, k_, q_]= (Binomial[3*q,2]/3)^(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=10}, Table[(m+2)^(k*(n-k)), {n,0,12}, {k,0,n}]//Flatten] (* _G. C. Greubel_, Jun 30 2021 *)
%o (Magma) [(12)^(k*(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 30 2021
%o (Sage) flatten([[(12)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 30 2021
%Y Cf. A000326,
%Y Cf. A118190 (q=2), this sequence (q=3), A176631 (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), this sequence (m=10), A176639 (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
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