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.
%I A134398 #13 Sep 08 2022 08:45:32
%S A134398 1,1,1,1,3,1,1,5,5,1,1,7,10,7,1,1,9,16,16,9,1,1,11,23,29,23,11,1,1,13,
%T A134398 31,47,47,31,13,1,1,15,40,71,86,71,40,15,1,1,17,50,102,146,146,102,50,
%U A134398 17,1,1,19,61,141,234,277,234,141,61,19,1
%N A134398 Triangle read by rows: T(n, k) = (k-1)*(n-k) + binomial(n-1,k-1).
%C A134398 Row sums = A116725: (1, 2, 5, 12, 26, 52, ...).
%H A134398 G. C. Greubel, <a href="/A134398/b134398.txt">Rows n = 1..100 of triangle, flattened</a>
%F A134398 T(n, k) = A077028(n,k) + A007318(n,k) - 1.
%F A134398 Let p(x, n) = (1+x)^n + (1/2) * Sum_{j=1..n-1} (n-j)*j*x^j*(1 + x^(n - 2*j)) with p(x, 0) = 1, then T(n, k) = Coefficients(p(x,n)). - _Roger L. Bagula_, Nov 02 2008
%F A134398 T(n, k) = (k-1)*(n-k) + binomial(n-1,k-1). - _G. C. Greubel_, Nov 29 2019
%e A134398 First few rows of the triangle are:
%e A134398 1;
%e A134398 1, 1;
%e A134398 1, 3, 1;
%e A134398 1, 5, 5, 1;
%e A134398 1, 7, 10, 7, 1;
%e A134398 1, 9, 16, 16, 9, 1;
%e A134398 1, 11, 23, 29, 23, 11, 1;
%e A134398 1, 13, 31, 47, 47, 31, 13, 1;
%e A134398 1, 15, 40, 71, 86, 71, 40, 15, 1;
%e A134398 ...
%p A134398 seq(seq( (k-1)*(n-k) + binomial(n-1,k-1), k=1..n), n=1..10); # _G. C. Greubel_, Nov 29 2019
%t A134398 p[x_, n_]:= p[x,n]= If[n==0, 1, (x+1)^n +Sum[(n-m)*m*x^m*(1 +x^(n-2*m)), {m, 1, n- 1}]/2]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]//Flatten (* _Roger L. Bagula_, Nov 02 2008 *)
%t A134398 Table[(k-1)*(n-k) + Binomial[n-1, k-1], {n,10}, {k,n}]//Flatten (* _G. C. Greubel_, Nov 29 2019 *)
%o A134398 (PARI) T(n,k) = (k-1)*(n-k) + binomial(n-1,k-1); \\ _G. C. Greubel_, Nov 29 2019
%o A134398 (Magma) [(k-1)*(n-k) + Binomial(n-1,k-1): k in [1..n], n in [1..10]]; // _G. C. Greubel_, Nov 29 2019
%o A134398 (Sage) [[(k-1)*(n-k) + binomial(n-1,k-1) for k in (1..n)] for n in (1..10)] # _G. C. Greubel_, Nov 29 2019
%o A134398 (GAP) Flat(List([1..10], n-> List([1..n], k-> (k-1)*(n-k) + Binomial(n-1,k-1) ))); # _G. C. Greubel_, Nov 29 2019
%Y A134398 Cf. A007318, A077028, A116725.
%K A134398 nonn,tabl
%O A134398 1,5
%A A134398 _Gary W. Adamson_, Oct 23 2007
%E A134398 Extended by _Roger L. Bagula_, Nov 02 2008
%E A134398 Edited by _G. C. Greubel_, Nov 29 2019