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%I #7 Sep 08 2022 08:45:53
%S 1,1,1,1,40,1,1,1600,1600,1,1,64000,2560000,64000,1,1,2560000,
%T 4096000000,4096000000,2560000,1,1,102400000,6553600000000,
%U 262144000000000,6553600000000,102400000,1,1,4096000000,10485760000000000,16777216000000000000,16777216000000000000,10485760000000000,4096000000,1
%N Triangle T(n, k) = 40^(k*(n-k)), read by rows.
%H G. C. Greubel, <a href="/A176644/b176644.txt">Rows n = 0..40 of the triangle, flattened</a>
%F T(n, k, q) = c(n,q)/(c(k, q)*c(n-k, q)) where c(n, q) = (q*(3*q - 2))^binomial(n+1,2) and q = 4.
%F T(n, k, q) = (q*(3*q-2))^(k*(n-k)) with q = 4.
%F T(n, k, m) = (m+2)^(k*(n-k)) with m = 38. - _G. C. Greubel_, Jul 01 2021
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 40, 1;
%e 1, 1600, 1600, 1;
%e 1, 64000, 2560000, 64000, 1;
%e 1, 2560000, 4096000000, 4096000000, 2560000, 1;
%e 1, 102400000, 6553600000000, 262144000000000, 6553600000000, 102400000, 1;
%t T[n_, k_, q_]:= (q*(3*q-2))^(k*(n-k)); Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten
%t Table[(40)^(k*(n-k)), {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 01 2021 *)
%o (Magma) [40^(k*(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 01 2021
%o (Sage) flatten([[40^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jul 01 2021
%Y Cf. A000567.
%Y Cf. A176642 (q=2), A176643 (q=3), this sequence (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), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26), this sequence (m=38).
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Apr 22 2010
%E Edited by _G. C. Greubel_, Jul 01 2021
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