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 A326723 #14 Apr 23 2024 08:11:14
%S A326723 0,-1,1,2,-4,2,-16,48,-48,16,272,-1088,1632,-1088,272,-7936,39680,
%T A326723 -79360,79360,-39680,7936,353792,-2122752,5306880,-7075840,5306880,
%U A326723 -2122752,353792,-22368256,156577792,-469733376,782888960,-782888960,469733376,-156577792,22368256
%N A326723 Triangle read by rows: T(n, k) = (-1)^(n - k) * binomial(n, k) * A000182(n).
%F A326723 T(n, k) = (2*n-1)! [x^k] [y^(2*n-1)] sqrt(x - 1)*tan(y*sqrt(x - 1)) for n > 0.
%F A326723 Sum_{k=0..n} (-1)^(n-k)*T(n, k) = 2*A261042(n-1) for n > 0.
%e A326723 Triangle starts:
%e A326723 [0] 0;
%e A326723 [1] -1, 1;
%e A326723 [2] 2, -4, 2;
%e A326723 [3] -16, 48, -48, 16;
%e A326723 [4] 272, -1088, 1632, -1088, 272;
%e A326723 [5] -7936, 39680, -79360, 79360, -39680, 7936;
%e A326723 [6] 353792, -2122752, 5306880, -7075840, 5306880, -2122752, 353792;
%p A326723 T := (n, k) -> (-1)^(n - k)*binomial(n, k)*A000182(n):
%p A326723 seq(seq(T(n, k), k = 0..n), n = 0..6); # _Peter Luschny_, Apr 23 2024
%t A326723 gf := Sqrt[x - 1] Tan[y Sqrt[x - 1]];
%t A326723 ser := Series[gf, {y, 0, 26}];
%t A326723 cy[n_] := n! Coefficient[ser, y, n];
%t A326723 row[n_] := If[n == 0, 0, CoefficientList[cy[2 n - 1], x]];
%t A326723 Table[row[n], {n, 0, 7}] // Flatten
%Y A326723 Cf. A000182, A261042, A326722.
%K A326723 sign,tabl
%O A326723 0,4
%A A326723 _Peter Luschny_, Aug 08 2019
%E A326723 Offset set to 0, T(0,0) = 0 and new name by _Peter Luschny_, Apr 23 2024