A159807 Numerator of Hermite(n, 3/22).

1, 3, -233, -2151, 162705, 2570283, -189162201, -4299537519, 307542155937, 9246531104595, -642087222317001, -24302866940070903, 1636327584987643953, 75484508348928834171, -4921433057324341373625, -270505813458143914292223, 17053284557712927443382081

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..435

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

Formula

From Vincenzo Librandi, Jan 20 2017: (Start)

Conjecture: E.g.f.: exp(-x*(121*x-3)).

D-finite with recurrence a(n) = 3*a(n-1) - 242*(n-1)*a(n-2). [DLMF] Corrected Feb 06 2021 (End)

Example

Numerators of 1, 3/11, -233/121, -2151/1331, 162705/14641, ...

Mathematica

Numerator/@HermiteH[Range[0, 20], 3/22]  (* Harvey P. Dale, May 01 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/22)) \\ Charles R Greathouse IV, Jan 29 2016
(SageMath) [numerator(hermite(n, 3/22)) for n in range(20)] # Bruno Berselli, Jan 19 2017
(Maxima) makelist(num(hermite(n, 3/22)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A099426 A332123 A100201 * A065580 A072320 A162603

Adjacent sequences: A159804 A159805 A159806 * A159808 A159809 A159810

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved