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.

A173476 Triangle T(n, k) = 1 + (k!)^2 - 2*k!*(n-k)! + ((n-k)!)^2, read by rows.

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%I A173476 #5 Feb 19 2021 18:34:45
%S A173476 1,1,1,2,1,2,26,2,2,26,530,26,1,26,530,14162,530,17,17,530,14162,
%T A173476 516962,14162,485,1,485,14162,516962,25391522,516962,13925,325,325,
%U A173476 13925,516962,25391522,1625621762,25391522,515525,12997,1,12997,515525,25391522,1625621762
%N A173476 Triangle T(n, k) = 1 + (k!)^2 - 2*k!*(n-k)! + ((n-k)!)^2, read by rows.
%H A173476 G. C. Greubel, <a href="/A173476/b173476.txt">Rows n = 0..100 of the triangle, flattened</a>
%F A173476 T(n, k) = 1 + ( (n-k)! - k! )^2.
%F A173476 Sum_{k=0..n} T(n, k) = 1 + n + 2*A061062(n) - 2*A003149(n). - _G. C. Greubel_, Feb 19 2021
%e A173476 Triangle begins as:
%e A173476            1;
%e A173476            1,        1;
%e A173476            2,        1,      2;
%e A173476           26,        2,      2,    26;
%e A173476          530,       26,      1,    26, 530;
%e A173476        14162,      530,     17,    17, 530, 14162;
%e A173476       516962,    14162,    485,     1, 485, 14162, 516962;
%e A173476     25391522,   516962,  13925,   325, 325, 13925, 516962, 25391522;
%e A173476   1625621762, 25391522, 515525, 12997,   1, 12997, 515525, 25391522, 1625621762;
%t A173476 Table[((n-k)! -k!)^2 +1, {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Feb 19 2021 *)
%o A173476 (Sage) flatten([[(factorial(n-k) -factorial(k))^2 +1 for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Feb 19 2021
%o A173476 (Magma) [(Factorial(n-k) -Factorial(k))^2 +1: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Feb 19 2021
%Y A173476 Cf. A003149, A061062.
%K A173476 nonn,tabl
%O A173476 0,4
%A A173476 _Roger L. Bagula_, Feb 19 2010
%E A173476 Edited by _G. C. Greubel_, Feb 19 2021