A159851 Numerator of Hermite(n, 19/22).

1, 19, 119, -6935, -218159, 2568059, 312765511, 2213723041, -487764037855, -13553284526621, 804837668442391, 48090864254828249, -1228751452551908111, -163002147394507489205, 768611269232660622311, 566854889488011925250449, 7980183992957668520769601

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

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

Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Formula

E.g.f.: exp(-x*(121*x-19)). - Simon Plouffe, Jun 22 2018

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 11^n * Hermite(n, 19/22).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -19*a(n-1) +242*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021

Example

Numerators of 1, 19/11, 119/121, -6935/1331, -218159/14641, ...

Mathematica

Numerator[Table[HermiteH[n, 19/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[11^n*HermiteH[n, 19/22], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/22)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 121*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A293879 A044351 A044732 * A221372 A252924 A157340

Adjacent sequences: A159848 A159849 A159850 * A159852 A159853 A159854

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved