The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A159545

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A159545

Numerator of Hermite(n, 1/18).
(history; published version)

#15 by Charles R Greathouse IV at Thu Sep 08 08:45:43 EDT 2022

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(1/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Discussion

Thu Sep 08

08:45

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

#14 by Alois P. Heinz at Tue Jun 12 15:10:54 EDT 2018

STATUS

reviewed

approved

#13 by Michel Marcus at Tue Jun 12 03:20:01 EDT 2018

STATUS

proposed

reviewed

#12 by G. C. Greubel at Sun Jun 10 14:58:12 EDT 2018

STATUS

editing

proposed

#11 by G. C. Greubel at Sun Jun 10 14:58:08 EDT 2018

FORMULA

a(n) = 189^n * Hermite(n,1/18).

E.g.f.: exp(2*x-32481*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/9)^(n-2k2*k)/(k!*(n-2k2*k)!)). (End)

STATUS

approved

editing

#10 by Susanna Cuyler at Sat Jun 09 18:59:51 EDT 2018

STATUS

proposed

approved

#9 by G. C. Greubel at Sat Jun 09 18:17:42 EDT 2018

STATUS

editing

proposed

#8 by G. C. Greubel at Sat Jun 09 18:16:50 EDT 2018

LINKS

G. C. Greubel, <a href="/A159545/b159545.txt">Table of n, a(n) for n = 0..450</a>

FORMULA

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 18^n * Hermite(n,1/18).

E.g.f.: exp(2*x-324*x^2).

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

PROG

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(1/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

STATUS

approved

editing

#7 by Charles R Greathouse IV at Fri Jan 29 13:31:47 EST 2016

STATUS

editing

approved

#6 by Charles R Greathouse IV at Fri Jan 29 13:31:45 EST 2016

PROG

(PARI) a(n)=numerator(polhermite(n, 1/18)) \\ Charles R Greathouse IV, Jan 29 2016

STATUS

approved

editing