login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160251 Numerator of Hermite(n, 8/29). 1
1, 16, -1426, -76640, 5969356, 611143616, -40423986104, -6814445150336, 366920889983120, 97565908182651136, -3993393901642052384, -1704952878058464945664, 46606527919245814078144, 35158473337439989488532480, -456562766083189138816177024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 29^n * Hermite(n, 8/29).

E.g.f.: exp(16*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 16/29, -1426/841, -76640/24389, 5969356/707281, ...

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 8/29]] (* Harvey P. Dale, Jul 22 2014 *)

Table[29^n*HermiteH[n, 8/29], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)

a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Exp[ 16 x - 841 x^2], {x, 0, n}]]; (* Michael Somos, Jul 30 2018 *)

PROG

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

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(16/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(16/29)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 12 2018

CROSSREFS

Cf. A009973 (denominators).

Sequence in context: A321583 A057994 A221607 * A106176 A263975 A193128

Adjacent sequences:  A160248 A160249 A160250 * A160252 A160253 A160254

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 December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)