OFFSET
0,3
LINKS
Winston de Greef, Table of n, a(n) for n = 0..628
FORMULA
a(n) = a(n-1) - 6*(n-1)*a(n-2) for n > 1.
a(n) = n! * Sum_{k=0..floor(n/2)} (-3)^k / (k! * (n-2*k)!).
a(n) = (-sqrt(3))^n * Hermite(n, 1/(2*sqrt(3))). - G. C. Greubel, Jul 12 2024
MATHEMATICA
With[{m=30}, CoefficientList[Series[Exp[x-3*x^2], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Jul 12 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-3*x))))
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!(Laplace( Exp(x-3*x^2) ))); // G. C. Greubel, Jul 12 2024
(SageMath)
[(-sqrt(3))^n*hermite(n, 1/(2*sqrt(3))) for n in range(31)] # G. C. Greubel, Jul 12 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Apr 10 2023
STATUS
approved