OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..732
FORMULA
a(n) = (-1)^n * A000321(n).
a(n) = a(n-1) - 2 * (n-1) * a(n-2) for n > 1.
E.g.f.: Product_{k>=1} (1 + x^k)^(mu(k)/k). - Ilya Gutkovskiy, May 23 2019
a(n) = Hermite(n, 1/2). - G. C. Greubel, Jul 12 2024
MATHEMATICA
CoefficientList[Series[E^(x*(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *)
PROG
(PARI) my(N=66, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x))))
(PARI) a(n) = polhermite(n, 1/2); \\ Michel Marcus, Oct 13 2017
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!(Laplace( Exp(x-x^2) ))); // G. C. Greubel, Jul 12 2024
(SageMath)
[hermite(n, 1/2) for n in range(31)] # G. C. Greubel, Jul 12 2024
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 12 2017
STATUS
approved