The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160107

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A160107

Numerator of Hermite(n, 7/27).
(history; published version)

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

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(14/27)^(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

#14 by Bruno Berselli at Tue Sep 25 03:57:47 EDT 2018

STATUS

reviewed

approved

#13 by Michel Marcus at Tue Sep 25 01:43:22 EDT 2018

STATUS

proposed

reviewed

#12 by Jon E. Schoenfield at Tue Sep 25 00:25:06 EDT 2018

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Tue Sep 25 00:25:04 EDT 2018

EXAMPLE

Numerators of 1, 14/27, -1262/729, -58492/19683, 4701100/531441, ...

STATUS

proposed

editing

#10 by G. C. Greubel at Mon Sep 24 23:24:44 EDT 2018

STATUS

editing

proposed

#9 by G. C. Greubel at Mon Sep 24 23:24:39 EDT 2018

LINKS

G. C. Greubel, <a href="/A160107/b160107.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, 7/27).

E.g.f.: exp(14*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

MATHEMATICA

Table[27^n*HermiteH[n, 7/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(14/27)^(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

#8 by Harvey P. Dale at Fri Jun 08 17:35:17 EDT 2018

STATUS

editing

approved

#7 by Harvey P. Dale at Fri Jun 08 17:35:14 EDT 2018

MATHEMATICA

HermiteH[Range[0, 20], 7/27]//Numerator (* Harvey P. Dale, Jun 08 2018 *)

STATUS

approved

editing

#6 by Charles R Greathouse IV at Fri Jan 29 15:30:51 EST 2016

STATUS

editing

approved