%I #4 Aug 20 2021 07:07:09
%S 0,1,-6,54,-552,6840,-97200,1577520,-28667520,578067840,-12798777600,
%T 308836281600,-8065907942400,226719600307200,-6824229456844800,
%U 219010610827008000,-7465397891567616000,269363867734241280000,-10256545055212904448000
%N E.g.f.: x/(1+3x-4x^3)=x/[1-T(3,x)], where T(3,x) is a Chebyshev polynomial.
%C "Bernoulli numbers" for x/[1-T(3,x)].
%F D-finite with recurrence a(n) +(n+4)*a(n-1) -2*n*(n-1)*a(n-2) -4*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Aug 20 2021
%p G:=x/(1+3*x-4*x^3): Gser:=series(G,x=0,23): 0,seq(n!*coeff(Gser,x^n),n=1..20); # yields the signed sequence
%t g[x_] = x/(-1 + ChebyshevT[3, x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = a[0]
%K sign
%O 0,3
%A _Roger L. Bagula_, Jun 28 2005