A159682 Numerator of Hermite(n, 19/20).

1, 19, 161, -4541, -182879, 158099, 185882881, 3342055939, -196736970559, -9085291943021, 181506000088801, 21619197887729219, 11451559671492961, -51668495296791759341, -1011475465784925126079, 125453752981103348759299, 5418047703995739004663681

Offset

0,2

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) -19*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 17 2014

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 10^n * Hermite(n,19/20).

E.g.f.: exp(19*x-100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/20)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 19/10, 161/100, -4541/1000, -182879/10000, 158099/100000,..

Maple

A159682 := proc(n)
        orthopoly[H](n, 19/20) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator[Table[HermiteH[n, 19/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/20)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 02 2018

Crossrefs

Cf. A011557 (denominators).

Sequence in context: A261791 A302124 A217215 * A197500 A341398 A212850

Adjacent sequences: A159679 A159680 A159681 * A159683 A159684 A159685

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved