cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A176644 Triangle T(n, k) = 40^(k*(n-k)), read by rows.

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