login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160037 Numerator of Hermite(n, 11/25). 1
1, 22, -766, -71852, 1291756, 387678632, 455454904, -2897569732112, -67731764516464, 27485598501757792, 1366665517848891424, -313503339879296788672, -25688724347766786430784, 4137398162538582528602752, 508464530227059095129500544, -61218248179429894157699148032 (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, 11/25).

E.g.f.: exp(22*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 22/25, -766/625, -71852/15625, 1291756/390625, ...

MAPLE

seq(coeff(series(factorial(n)*exp(22*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 11/25]] (* Harvey P. Dale, Dec 27 2011 *)

Table[25^n* HermiteH[n, 11/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 11/25)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018

(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/25)^(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)*(22/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

CROSSREFS

Cf. A009969 (denominators).

Sequence in context: A159189 A067768 A181181 * A278440 A152957 A237605

Adjacent sequences: A160034 A160035 A160036 * A160038 A160039 A160040

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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 01:31 EST 2022. Contains 358431 sequences. (Running on oeis4.)