A012303 - OEIS

%I #11 Sep 08 2022 08:44:38

%S 1,0,-12,240,4368,-942720,42639168,8638506240,-2287049555712,

%T 38746394603520,145600412857955328,-42974022434701332480,

%U -7760313189299657306112,11863589839842518338928640

%N Expansion of e.g.f. sech(sin(x)*sin(x)), even powers only.

%H G. C. Greubel, <a href="/A012303/b012303.txt">Table of n, a(n) for n = 0..225</a>

%e E.g.f. = 1 - 12*x^4/4! + 240*x^6/6! + 4368*x^8/8! + ...

%p seq(coeff(series(factorial(n)*sech(sin(x)*sin(x)),x,n+1), x, n), n = 0 .. 26,2); # _Muniru A Asiru_, Oct 26 2018

%t With[{nn = 100}, CoefficientList[Series[Sech[Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* _G. C. Greubel_, Oct 25 2018 *)

%o (PARI) x='x+O('x^50); v=Vec(serlaplace(1/cosh(sin(x)*sin(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Oct 25 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cosh(Sin(x)^2) ));  [Factorial(2*n)*b[2*n+1]: n in [0..Floor((m-2)/2)]];  // _G. C. Greubel_, Oct 25 2018

%K sign

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)