The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160012

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A160012

Numerator of Hermite(n, 8/25).
(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)*(16/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 17 2018

Discussion

Thu Sep 08

08:45

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

#13 by Susanna Cuyler at Tue Jul 17 08:10:26 EDT 2018

STATUS

proposed

approved

#12 by Muniru A Asiru at Tue Jul 17 05:59:18 EDT 2018

STATUS

editing

proposed

#11 by Muniru A Asiru at Tue Jul 17 05:57:18 EDT 2018

MAPLE

seq(coeff(series(factorial(n)*exp(16*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

PROG

(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(16/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

STATUS

proposed

editing

#10 by G. C. Greubel at Tue Jul 17 02:30:13 EDT 2018

STATUS

editing

proposed

#9 by G. C. Greubel at Tue Jul 17 02:30:09 EDT 2018

LINKS

G. C. Greubel, <a href="/A160012/b160012.txt">Table of n, a(n) for n = 0..380</a>

FORMULA

From G. C. Greubel, Jul 17 2018: (Start)

a(n) = 25^n * Hermite(n, 8/25).

E.g.f.: exp(16*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

MATHEMATICA

Table[25^n*HermiteH[n, 8/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(16/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 17 2018

STATUS

approved

editing

#8 by Charles R Greathouse IV at Fri Jan 29 15:20:35 EST 2016

STATUS

editing

approved

#7 by Charles R Greathouse IV at Fri Jan 29 15:20:05 EST 2016

PROG

(PARI) a(n)=numerator(polhermite(n, 8/25)) \\ Charles R Greathouse IV, Jan 29 2016

STATUS

approved

editing

#6 by R. J. Mathar at Sat Feb 22 11:53:28 EST 2014

STATUS

editing

approved

#5 by R. J. Mathar at Sat Feb 22 11:53:23 EST 2014

EXAMPLE

Numerators of 1, 16/25, -994/625, -55904/15625, 2833036/390625

CROSSREFS

The denominators are an easily recognizable sequence.

Cf. A009969 (denominators).

STATUS

approved

editing