The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160300 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A160300

Numerator of Hermite(n, 2/31).
(history; published version)

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

PROG

(MAGMAMagma) [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

Discussion

Thu Sep 08

08:45

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

#16 by Bruno Berselli at Fri Oct 05 03:50:36 EDT 2018

STATUS

reviewed

approved

#15 by Michel Marcus at Fri Oct 05 02:03:02 EDT 2018

STATUS

proposed

reviewed

#14 by G. C. Greubel at Fri Oct 05 00:10:12 EDT 2018

STATUS

editing

proposed

#13 by G. C. Greubel at Fri Oct 05 00:10:07 EDT 2018

LINKS

G. C. Greubel, <a href="/A160300/b160300.txt">Table of n, a(n) for n = 0..368</a>

FORMULA

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)

MATHEMATICA

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

PROG

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

STATUS

approved

editing

#12 by Susanna Cuyler at Wed Mar 28 22:05:09 EDT 2018

STATUS

proposed

approved

#11 by Jon E. Schoenfield at Wed Mar 28 18:42:55 EDT 2018

STATUS

editing

proposed

#10 by Jon E. Schoenfield at Wed Mar 28 18:42:53 EDT 2018

EXAMPLE

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

STATUS

proposed

editing

#9 by Bruno Berselli at Wed Mar 28 09:53:57 EDT 2018

STATUS

editing

proposed

#8 by Bruno Berselli at Wed Mar 28 09:50:28 EDT 2018

FORMULA

a(n+2) = 4*a(n+1) - 1922*(n+1)*a(n). - Bruno Berselli, Mar 28 2018