The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160153 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A160153

Numerator of Hermite(n, 26/27).
(history; published version)

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

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(52/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Discussion

Thu Sep 08

08:45

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

#13 by Bruno Berselli at Tue Sep 25 03:59:12 EDT 2018

STATUS

reviewed

approved

#12 by Michel Marcus at Tue Sep 25 02:55:40 EDT 2018

STATUS

proposed

reviewed

#11 by Jon E. Schoenfield at Tue Sep 25 00:33:49 EDT 2018

STATUS

editing

proposed

#10 by Jon E. Schoenfield at Tue Sep 25 00:33:47 EDT 2018

CROSSREFS

Cf. A009971 (denominators).

#9 by Jon E. Schoenfield at Tue Sep 25 00:33:35 EDT 2018

EXAMPLE

Numerators of 1, 52/27, 1246/729, -86840/19683, -9965684/531441, ...

STATUS

proposed

editing

#8 by G. C. Greubel at Tue Sep 25 00:03:21 EDT 2018

STATUS

editing

proposed

#7 by G. C. Greubel at Tue Sep 25 00:03:16 EDT 2018

LINKS

G. C. Greubel, <a href="/A160153/b160153.txt">Table of n, a(n) for n = 0..376</a>

FORMULA

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 26/27).

E.g.f.: exp(52*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

MATHEMATICA

Table[27^n*HermiteH[n, 26/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(exp(52*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(52/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

STATUS

approved

editing

#6 by Charles R Greathouse IV at Fri Jan 29 15:34:19 EST 2016

STATUS

editing

approved

#5 by Charles R Greathouse IV at Fri Jan 29 15:34:09 EST 2016

PROG

(PARI) a(n)=numerator(polhermite(n, 26/27)) \\ Charles R Greathouse IV, Jan 29 2016

STATUS

approved

editing