%I #8 Jul 13 2018 03:36:27
%S 0,1,-24,864,-41280,2465280,-176670720,14770990080,-1411388375040,
%T 151717608161280,-18121032076492800,2380798038166732800,
%U -341232779553826406400,52983548082050826240000,-8859638774461689652838400,1587282455497648568795136000
%N E.g.f.: x/(1 + 12*x - 8*x^3) = x/[1-Hermite(3,x)].
%C "Bernoulli numbers" for x/[1-Hermite(3,x)].
%H G. C. Greubel, <a href="/A109575/b109575.txt">Table of n, a(n) for n = 0..317</a>
%p G:=x/(1+12*x-8*x^3): Gser:=series(G,x=0,20): 0,seq(n!*coeff(Gser,x^n),n=1..16); # yields the signed sequence
%t g[x_] = x/(-1 + HermiteH[3, x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = a[0]
%t With[{nmax = 50}, CoefficientList[Series[x/(1 + 12*x - 8*x^3), {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 12 2018 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(x/(1 + 12*x - 8*x^3)))) \\ _G. C. Greubel_, Jul 12 2018
%K sign
%O 0,3
%A _Roger L. Bagula_, Jun 28 2005