A302908 Expansion of e.g.f. 6*exp(-x)/(6 + x*(3 + x)*(6 + x)).

1, -4, 22, -164, 1589, -19136, 276224, -4650752, 89486849, -1937066524, 46589361346, -1232598278044, 35574999098357, -1112321525118584, 37454195074337084, -1351244122522567256, 51999107708388285089, -2126115743789144316212, 92045274930441985100494

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: 1 / Sum_{k>=0} ((k + 1)*(k + 2)*(k + 3)/6)*x^k/k! = 1 / Sum_{k>=0} A000292(k+1)*x^k/k!.

D-finite with recurrence +6*a(n) +6*(3*n+1)*a(n-1) +9*(n+2)*(n-1)*a(n-2) +(n-1)*(n-2)*(n+9)*a(n-3) +(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Aug 20 2021

Example

6*exp(-x)/(6 + x*(3 + x)*(6 + x)) = 1 - 4*x/1! + 22*x^2/2! - 164*x^3/3! + 1589*x^4/4! - 19136*x^5/5! + 276224*x^6/6! - 4650752*x^7/7! + ...

Maple

a:=series(6*exp(-x)/(6 + x*(3 + x)*(6 + x)), x=0, 19): seq(n!*coeff(a, x, n), n=0..18); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 18; CoefficientList[Series[6 Exp[-x]/(6 + x (3 + x) (6 + x)), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) x='x+O('x^99); Vec(serlaplace(6*exp(-x)/(6+x*(3+x)*(6+x)))) \\ Altug Alkan, Apr 15 2018

Crossrefs

Cf. A000292, A302195.

Sequence in context: A053144 A089464 A111343 * A187123 A121397 A067369

Adjacent sequences: A302905 A302906 A302907 * A302909 A302910 A302911

Keyword

sign

Author

Ilya Gutkovskiy, Apr 15 2018

Status

approved