OFFSET
0,7
LINKS
Robert Israel, Table of n, a(n) for n = 0..691
FORMULA
(n+3)*(n+2)*(n+1)*a(n) - a(n+4) - a(n+5) = 0.
Sum_{k=0..n} (2*k-n)*binomial(n,k)*a(k)*A318355(n-k) = (-1)^(n+1)*n. - Robert Israel, Aug 26 2018
MAPLE
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):
map(f, [$0..30]);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Robert Israel, Aug 24 2018
STATUS
approved