The On-Line Encyclopedia of Integer Sequences (OEIS)

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A160311

Numerator of Hermite(n, 13/31).
(history; published version)

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

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(26/31)^(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

#14 by Bruno Berselli at Fri Oct 05 05:40:08 EDT 2018

STATUS

reviewed

approved

#13 by Michel Marcus at Fri Oct 05 05:30:02 EDT 2018

STATUS

proposed

reviewed

#12 by Michel Marcus at Fri Oct 05 05:29:57 EDT 2018

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Fri Oct 05 01:18:16 EDT 2018

EXAMPLE

Numerators of 1, 26/31, -1246/961, -132340/29791, 3743596/923521, ...

STATUS

proposed

editing

#10 by G. C. Greubel at Fri Oct 05 01:02:07 EDT 2018

STATUS

editing

proposed

#9 by G. C. Greubel at Fri Oct 05 01:01:38 EDT 2018

LINKS

G. C. Greubel, <a href="/A160311/b160311.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, 13/31).

a(n+2) = 26*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(26*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

MATHEMATICA

Table[31^n*HermiteH[n, 13/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(26/31)^(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

#8 by Charles R Greathouse IV at Fri Jan 29 15:39:50 EST 2016

STATUS

editing

approved

#7 by Charles R Greathouse IV at Fri Jan 29 15:39:42 EST 2016

PROG

(PARI) a(n)=numerator(polhermite(n, 13/31)) \\ Charles R Greathouse IV, Jan 29 2016

STATUS

approved

editing

#6 by Harvey P. Dale at Sat Jan 10 09:43:45 EST 2015

STATUS

editing

approved