The On-Line Encyclopedia of Integer Sequences (OEIS)

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A159831

Numerator of Hermite(n, 9/22).
(history; published version)

#20 by Charles R Greathouse IV at Thu Sep 08 08:45:44 EDT 2022

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(9/11)^(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

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#19 by Susanna Cuyler at Wed Jul 11 15:36:54 EDT 2018

STATUS

proposed

approved

#18 by G. C. Greubel at Wed Jul 11 12:23:14 EDT 2018

STATUS

editing

proposed

#17 by G. C. Greubel at Wed Jul 11 12:22:47 EDT 2018

FORMULA

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 11^n * Hermite(n, 9/22).

E.g.f.: exp(9*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

MATHEMATICA

Table[11^n*HermiteH[n, 9/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(9/11)^(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

STATUS

approved

editing

#16 by Joerg Arndt at Sun May 20 03:26:12 EDT 2018

STATUS

reviewed

approved

#15 by Michel Marcus at Sun May 20 01:21:56 EDT 2018

STATUS

proposed

reviewed

#14 by Jon E. Schoenfield at Sat May 19 22:57:17 EDT 2018

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Sat May 19 22:57:13 EDT 2018

EXAMPLE

Numerators of 1, 9/11, -161/121, -5805/1331, 64641/14641, ...

CROSSREFS

Cf. A001020 (denominators).

STATUS

proposed

editing

#12 by G. C. Greubel at Sat May 19 22:55:08 EDT 2018

STATUS

editing

proposed

#11 by G. C. Greubel at Sat May 19 22:55:01 EDT 2018

LINKS

G. C. Greubel, <a href="/A159831/b159831.txt">Table of n, a(n) for n = 0..435</a>

STATUS

approved

editing