OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{m=0..n} A060821(n, m) = H(n, 1), with the Hermite polynomials H(n, x).
E.g.f.: exp(-x*(x-2)).
a(n) = 2*(a(n - 1) - (n - 1)*a(n - 2)). - Roger L. Bagula, Sep 11 2006
a(n) = 2^n * U(-n/2, 1/2, 1), where U is the confluent hypergeometric function. - Benedict W. J. Irwin, Oct 17 2017
E.g.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^(mu(k)/k). - Ilya Gutkovskiy, May 26 2019
MAPLE
MATHEMATICA
lst={}; Do[p=HermiteH[n, 1]; AppendTo[lst, p], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 15 2009 *)
Table[2^n HypergeometricU[-n/2, 1/2, 1], {n, 0, 23}] (* Benedict W. J. Irwin, Oct 17 2017 *)
With[{nmax=50}, CoefficientList[Series[Exp[x*(2-x)], {x, 0, nmax}], x]* Range[0, nmax]!] (* G. C. Greubel, Jun 08 2018 *)
PROG
(Python)
from sympy import hermite, Poly
def a(n): return sum(Poly(hermite(n, x), x).all_coeffs()) # Indranil Ghosh, May 26 2017
(PARI) x='x+O('x^30); Vec(serlaplace(exp(-x*(x-2)))) \\ G. C. Greubel, Jun 08 2018
(PARI) a(n) = polhermite(n, 1); \\ Michel Marcus, Jun 09 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x*(2-x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jun 08 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Jun 19 2001
STATUS
approved