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A160300 Numerator of Hermite(n, 2/31). 1
1, 4, -1906, -23000, 10897996, 220415984, -103848077624, -2957229437984, 1385343118601360, 51011732312847424, -23759618336314935584, -1075483968398187231616, 498023914992777619190464, 26797057907106900786753280, -12336437308381113989945920384 (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) = 4*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, 2/31).

E.g.f.: exp(4*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 4/31, -1906/961, -23000/29791, 10897996/923521, ...

MATHEMATICA

Table[31^n*HermiteH[n, 2/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 2/31)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

(Maxima) makelist(num(hermite(n, 2/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */

(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/31)^(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: A255268 A079402 A198975 * A024060 A198716 A004815

Adjacent sequences: A160297 A160298 A160299 * A160301 A160302 A160303

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified December 5 09:04 EST 2022. Contains 358585 sequences. (Running on oeis4.)