A318356 E.g.f. satisfies y'' + y' - x^3*y = 0 with y(0)=0, y'(0)=1.

0, 1, -1, 1, -1, 1, 23, -83, 203, -413, 749, 10843, -70603, 271573, -816733, 2102017, 21579095, -214325285, 1126810565, -4459081205, 14750556437, 110710301893, -1576695251293, 10568643559993, -51770553894193, 208509966593755, 1135955939594837, -22894350407438237, 187765189943329037

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

Cf. A318237, A318293, A318355.

Sequence in context: A128825 A339475 A167573 * A142790 A288340 A316378

Adjacent sequences: A318353 A318354 A318355 * A318357 A318358 A318359

Keyword

sign

Author

Robert Israel, Aug 24 2018

Status

approved