A160077 Numerator of Hermite(n, 19/26).

1, 19, 23, -12407, -259055, 11852219, 662995111, -11439393023, -1785994900063, -3001784367005, 5375962583018551, 112289320237829369, -17854331799144214607, -794677787068375998197, 63353055971140535017415, 4964123351859225388799089, -226881650088357230151111359

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

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) +338*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

E.g.f.: exp(-x*(169*x-19)). The conjecture is a consequence. - Robert Israel, Jan 02 2017

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

a(n) = 13^n * Hermite(n, 19/26).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 19/13, 23/169, -12407/2197, -259055/28561, 11852219/371293,...

Maple

A160077 := proc(n)
        orthopoly[H](n, 19/26) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

f[n_] := HermiteH[n, 19/26]*13^n; Array[f, 17, 0] (* Robert G. Wilson v, Nov 13 2011 *)
HermiteH[Range[0, 30], 19/26]//Numerator (* Harvey P. Dale, Feb 02 2017 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/26)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/13)^(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. A001022 (denominators)

Sequence in context: A240585 A226607 A284495 * A076353 A297575 A093020

Adjacent sequences: A160074 A160075 A160076 * A160078 A160079 A160080

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved