A159676 Numerator of Hermite(n, 17/20).

1, 17, 89, -5287, -143279, 1793857, 173774569, 801539273, -229658228959, -5186652729103, 325211715731449, 15901904625640633, -445133395973297039, -45731838833083568863, 379905569368151630729, 134507543411892570538793, 1146911529897718806972481

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

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 10^n * Hermite(n, 17/20).

E.g.f.: exp(17*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 17/10, 89/100, -5287/1000, -143279/10000, 1793857/100000,...

Maple

A159676 := proc(n)
        orthopoly[H](n, 17/20) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator/@Table[HermiteH[n, 17/20], {n, 0, 35}]  (* Harvey P. Dale, Mar 13 2011 *)
Table[10^n*HermiteH[n, 17/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/10)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Crossrefs

Cf. A011557 (denominators).

Sequence in context: A267820 A200670 A057638 * A061971 A061222 A228462

Adjacent sequences: A159673 A159674 A159675 * A159677 A159678 A159679

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved