A062267 Row sums of (signed) triangle A060821 (Hermite polynomials).

1, 2, 2, -4, -20, -8, 184, 464, -1648, -10720, 8224, 230848, 280768, -4978816, -17257600, 104891648, 727511296, -1901510144, -28538404352, 11377556480, 1107214478336, 1759326697472, -42984354695168, -163379084079104

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..730

Index entries for sequences related to Hermite polynomials

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

A062267 := proc(n)
    HermiteH(n, 1) ;
    simplify(%) ;
end proc: # R. J. Mathar, Feb 05 2013

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

Cf. A000898, A121966.

Sequence in context: A120417 A175185 A257610 * A128501 A288497 A288767

Adjacent sequences: A062264 A062265 A062266 * A062268 A062269 A062270

Keyword

sign,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved