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 A009562 #32 Apr 16 2025 09:02:02
%S A009562 1,2,-4,-624,-37808,-2529440,-197245632,-17275207936,-1517532372736,
%T A009562 -78275049887232,24598365340871680,16151599386896207872,
%U A009562 7394065277787966590976,3266488097334689885904896,1491592302825720723705577472,718708462133271426457747783680
%N A009562 Expansion of e.g.f. sin(x/cos(x)) (odd powers only).
%H A009562 G. C. Greubel, <a href="/A009562/b009562.txt">Table of n, a(n) for n = 1..240</a>
%F A009562 a(n+1) = (-1)^n + 2*Sum_{m=0..n-1} binomial(2*n+1, 2*m+1)*Sum_{j=0..n-m} binomial(m+j-1/2, j)*4^(n-m-j)*Sum_{i=0..j} (i-j)^(2*n-2*m)*binomial(2*j, i)*(-1)^(n+j-i). - _Vladimir Kruchinin_, Jun 29 2011
%t A009562 With[{nmax = 50}, CoefficientList[Series[Sin[x/Cos[x]], {x, 0, nmax}], x]*Range[0, nmax - 1]!][[2 ;; ;; 2]] (* _G. C. Greubel_, Jan 21 2018 *)
%o A009562 (Maxima) a(n):=2*(sum(binomial(2*n+1, 2*m+1)*sum(binomial(m+j-1/2, j)* 4^(n-m-j)*sum((i-j)^(2*n-2*m)*binomial(2*j, i)*(-1)^(n+j-i), i, 0, j), j, 0, n-m), m, 0, n-1))+(-1)^(n); /* _Vladimir Kruchinin_, Jun 29 2011 */
%o A009562 (PARI) my(v=sin(x/cos(x))); forstep(n=1,default(seriesprecision),2,print1(polcoeff(v,n)*n!", ")) \\ _Charles R Greathouse IV_, Jun 27 2011
%K A009562 sign
%O A009562 1,2
%A A009562 _R. H. Hardin_
%E A009562 Extended with signs by _Olivier Gérard_, Mar 15 1997
%E A009562 a(15)-a(16) from _G. C. Greubel_, Jan 21 2018