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%I #7 Sep 08 2022 08:45:53
%S 1,1,1,1,21,1,1,441,441,1,1,9261,194481,9261,1,1,194481,85766121,
%T 85766121,194481,1,1,4084101,37822859361,794280046581,37822859361,
%U 4084101,1,1,85766121,16679880978201,7355827511386641,7355827511386641,16679880978201,85766121,1
%N Triangle T(n, k) = 21^(k*(n-k)), read by rows.
%H G. C. Greubel, <a href="/A176643/b176643.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, q) = (q*(3*q - 2))^binomial(n+1,2) and q = 3.
%F T(n, k, q) = (q*(3*q-2))^(k*(n-k)) with q = 3.
%F T(n, k, m) = (m+2)^(k*(n-k)) with m = 19. - _G. C. Greubel_, Jul 01 2021
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 21, 1;
%e 1, 441, 441, 1;
%e 1, 9261, 194481, 9261, 1;
%e 1, 194481, 85766121, 85766121, 194481, 1;
%e 1, 4084101, 37822859361, 794280046581, 37822859361, 4084101, 1;
%t T[n_, k_, q_]:= (q*(3*q-2))^(k*(n-k)); Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten
%t Table[21^(k*(n-k)), {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 01 2021 *)
%o (Magma) [(21)^(k*(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 01 2021
%o (Sage) flatten([[(21)^(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), this sequence (q=3), A176644 (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), this sequence (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_, Jul 01 2021
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