A318356 - OEIS

%I #17 Apr 27 2019 03:37:50

%S 0,1,-1,1,-1,1,23,-83,203,-413,749,10843,-70603,271573,-816733,

%T 2102017,21579095,-214325285,1126810565,-4459081205,14750556437,

%U 110710301893,-1576695251293,10568643559993,-51770553894193,208509966593755,1135955939594837,-22894350407438237,187765189943329037

%N E.g.f. satisfies y'' + y' - x^3*y = 0 with y(0)=0, y'(0)=1.

%H Robert Israel, <a href="/A318356/b318356.txt">Table of n, a(n) for n = 0..691</a>

%F (n+3)*(n+2)*(n+1)*a(n) - a(n+4) - a(n+5) = 0.

%F Sum_{k=0..n} (2*k-n)*binomial(n,k)*a(k)*A318355(n-k) = (-1)^(n+1)*n. - _Robert Israel_, Aug 26 2018

%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, A318293, A318355.

%K sign

%O 0,7

%A _Robert Israel_, Aug 24 2018