login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160010 Numerator of Hermite(n, 6/25). 1
1, 12, -1106, -43272, 3628236, 259898832, -19557689016, -2183933508192, 144922576791696, 23578406003420352, -1347438116865535776, -310899332445140829312, 14796482117559426968256, 4841047772087825563299072, -182350261145286781474571136, -86906539145280388735428613632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..380

FORMULA

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

a(n) = 25^n * Hermite(n, 6/25).

E.g.f.: exp(12*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 12/25, -1106/625, -43272/15625, 3628236/390625

MAPLE

seq(coeff(series(factorial(n)*exp(12*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

MATHEMATICA

Numerator[Table[HermiteH[n, 6/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 6/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 6/25)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(12/25)^(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

(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(12/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

CROSSREFS

Cf. A009969 (denominators).

Sequence in context: A274117 A295427 A260030 * A325906 A181718 A004073

Adjacent sequences:  A160007 A160008 A160009 * A160011 A160012 A160013

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)