%I #9 Mar 02 2024 00:02:49

%S 1,7,-84,1020,-17220,313068,-6075444,122709468,-2553130020,

%T 54317619660,-1175968479252,25819593611196,-573476704909572,

%U 12861006710141100,-290799326551852020,6621725329384239516,-151707434284857934308,3494405505576163607436

%N Expansion of ( (1 + x)*(1 - 5*x)*(1 + 25*x) )^(1/3).

%C The cube root of F(x) = (1 + x)*(1 - (3*k+2)*x)*(1 + (3*k+2)^2*x) is an integer series because F(x) == (1+x)*(1 + 2*x - 8*x^2) == (1+x)^3 (mod 9).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(((1+x)*(1-5*x)*(1+25*x))^(1/3))

%Y Cf. A370145, A370149, A370780.

%Y Cf. A370782.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 01 2024