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%I #14 Apr 27 2019 03:38:06
%S 0,1,-1,1,-1,1,-25,85,-205,415,-751,13351,-74551,277501,-825301,
%T 2114017,-31272601,234796831,-1167200191,4534428271,-14884655503,
%U 196703557717,-1802713881757,11116971405937,-53015088629977,211179438004855,-2599947442920103,27477399011166703,-200902152943783903
%N E.g.f. satisfies y'' + y' + x^3*y = 0 with y(0)=0, y'(0)=1.
%H Robert Israel, <a href="/A318293/b318293.txt">Table of n, a(n) for n = 0..690</a>
%F (n+3)*(n+2)*(n+1)*a(n) + a(n+4) + a(n+5) = 0.
%p f:= gfun:-rectoproc({(n+3)*(n+2)*(n+1)*a(n)+a(n+4)+a(n+5)=0, a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 1, a(4) = -1}, a(n), remember):
%p map(f, [$0..30]);
%t m = 30; egf = DifferentialRoot[Function[{y, x}, {y''[x] + y'[x] + x^3*y[x] == 0, y[0] == 0, y'[0] == 1}]]; CoefficientList[egf[x] + O[x]^m, x]* Range[0, m-1]! (* _Jean-François Alcover_, Apr 27 2019 *)
%Y Cf. A318237, A318355, A318356.
%K sign
%O 0,7
%A _Robert Israel_, Aug 23 2018