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%I #17 Sep 08 2022 08:46:22
%S 1,0,0,0,0,6,-6,6,-6,6,2010,-5034,9354,-15294,23214,3425946,-14420202,
%T 39956622,-91344462,186057582,16587374034,-100426428462,373729722942,
%U -1102658529702,2821830587382,173435605897902,-1393014153140430,6550484329740030,-23751957393091230,73275084201645330
%N E.g.f. satisfies y'' + y' - x^3*y = 0 with y(0)=1, y'(0)=0.
%H Robert Israel, <a href="/A318355/b318355.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)*A318356(n-k) = (-1)^n * 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) = 1, a(1) = 0, a(2) = 0, a(3) = 0, a(4) = 0}, 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] == 1, y'[0] == 0}]]; CoefficientList[egf[x] + O[x]^m, x]* Range[0, m-1]! (* _Jean-François Alcover_, Apr 27 2019 *)
%o (Magma) I:=[1,0,0,0,0]; [n le 5 select I[n] else (n-3)*(n-4)*(n-5)*Self(n-5)-Self(n-1): n in [1..30]]; // _Vincenzo Librandi_, Aug 26 2018
%Y Cf. A318237, A318293, A318356.
%K sign
%O 0,6
%A _Robert Israel_, Aug 24 2018
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