A318355 E.g.f. satisfies y'' + y' - x^3*y = 0 with y(0)=1, y'(0)=0.

1, 0, 0, 0, 0, 6, -6, 6, -6, 6, 2010, -5034, 9354, -15294, 23214, 3425946, -14420202, 39956622, -91344462, 186057582, 16587374034, -100426428462, 373729722942, -1102658529702, 2821830587382, 173435605897902, -1393014153140430, 6550484329740030, -23751957393091230, 73275084201645330

Offset

0,6

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)*A318356(n-k) = (-1)^n * 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) = 1, a(1) = 0, a(2) = 0, a(3) = 0, a(4) = 0}, 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] == 1, y'[0] == 0}]]; CoefficientList[egf[x] + O[x]^m, x]* Range[0, m-1]! (* Jean-François Alcover, Apr 27 2019 *)

Prog

(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

Crossrefs

Cf. A318237, A318293, A318356.

Sequence in context: A245399 A243758 A378372 * A318237 A201572 A261468

Adjacent sequences: A318352 A318353 A318354 * A318356 A318357 A318358

Keyword

sign

Author

Robert Israel, Aug 24 2018

Status

approved