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 A371688 #9 Apr 07 2024 03:36:37
%S A371688 1,-1,3,5,-50,25,-61,1281,-2135,427,1385,-49860,174510,-116340,12465,
%T A371688 -50521,2778655,-16671930,23340702,-8335965,555731,2702765,-210815670,
%U A371688 1932476975,-4637944740,3478458555,-772990790,35135945
%N A371688 Triangle read by rows: T(n, k) = (2*n + 1)! * [y^(2*k)] [x^(2*n+1)] arctan(sec(x*y)*sinh(x)).
%C A371688 Expansion of the exponential generating function arctan(sec(x*y)*sinh(x)), nonzero terms only.
%F A371688 T(n, k) = (-1)^k*binomial(2*n + 1, 2*k)*Euler(2*n). - _Detlef Meya_, Apr 07 2024
%e A371688 Triangle starts:
%e A371688 [0] 1;
%e A371688 [1] -1, 3;
%e A371688 [2] 5, -50, 25;
%e A371688 [3] -61, 1281, -2135, 427;
%e A371688 [4] 1385, -49860, 174510, -116340, 12465;
%e A371688 [5] -50521, 2778655, -16671930, 23340702, -8335965, 555731;
%p A371688 egf := arctan(sec(x*y)*sinh(x)):
%p A371688 serx := simplify(series(egf, x, 26)): coeffx := n -> n!*coeff(serx, x, n):
%p A371688 seq(lprint(seq(coeff(coeffx(2*n + 1), y, 2*k), k = 0..n)), n = 0..7);
%t A371688 T[n_,k_]:=(-1)^k*Binomial[2*n+1,2*k]*EulerE[2*n];Flatten[Table[T[n,k],{n,0,6},{k,0,n}]] (* _Detlef Meya_, Apr 07 2024 *)
%Y A371688 Cf. A000364 (column 0), A009843 (main diagonal), A012816 (row sums), A002436 (alternating row sums).
%K A371688 sign,tabl
%O A371688 0,3
%A A371688 _Peter Luschny_, Apr 03 2024