A159657 Numerator of Hermite(n, 1/20).

1, 1, -199, -599, 118801, 598001, -118202999, -835804199, 164648394401, 1501935112801, -294865174808999, -3298735400410999, 645404649179386801, 8562369610165784401, -1669489718256239898199, -25644124626720436220999, 4982825030141999258376001

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Formula

D-finite with recurrence a(n) -a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 09 2018: (Start)

a(n) = 10^n * Hermite(n, 1/20).

E.g.f.: exp(x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 1/10, -199/100, -599/1000, 118801/10000, 598001/100000,...

Maple

A159657 := proc(n)
        orthopoly[H](n, 1/20) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 1/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[10^n*HermiteH[n, 1/20], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/10)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Crossrefs

Cf. A011557 (denominators).

Sequence in context: A105975 A095995 A358898 * A308794 A308802 A142570

Adjacent sequences: A159654 A159655 A159656 * A159658 A159659 A159660

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved