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A160305 Numerator of Hermite(n, 7/31). 1
1, 14, -1726, -77980, 8860396, 723555784, -75018624584, -9394306045264, 877780290519440, 156735773819251424, -12989542631935753184, -3194315169653112913856, 229904497949242113022144, 76892348044168785827484800, -4667900913141400434386502784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..368

FORMULA

a(n+2) = 14*a(n+1) - 1922*(n+1)*a(n). - Bruno Berselli, Mar 28 2018

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 7/31).

E.g.f.: exp(14*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 14/31, -1726/961, -77980/29791, 8860396/923521, ...

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 7/31]] (* Harvey P. Dale, Apr 23 2016 *)

Table[31^n*HermiteH[n, 7/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 7/31)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

(Maxima) makelist(num(hermite(n, 7/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(14/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

CROSSREFS

Cf. A009975 (denominators).

Sequence in context: A322848 A206644 A060614 * A279804 A198601 A233076

Adjacent sequences:  A160302 A160303 A160304 * A160306 A160307 A160308

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified September 23 19:44 EDT 2021. Contains 347617 sequences. (Running on oeis4.)