|
| |
|
|
A362177
|
|
Expansion of e.g.f. exp(x * (1-3*x)).
|
|
10
|
|
|
|
1, 1, -5, -17, 73, 481, -1709, -19025, 52753, 965953, -1882709, -59839889, 64418905, 4372890913, -651783677, -367974620369, -309314089439, 35016249465985, 66566286588763, -3715188655737617, -11303745326856599, 434518893361657441, 1858790804545588915
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
STATUS
|
approved
|
| |
|
|
