A160084 Numerator of Hermite(n, 25/26).

1, 25, 287, -9725, -534143, -205375, 897567295, 22855682875, -1552252148095, -100608070196375, 2206749279595615, 395224009253637875, 1675906409804450305, -1561130921287643963375, -46392205796871853724545, 6227466374611334891576875, 390895142755423670672865025

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..422

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 13^n * Hermite(n, 25/26).

E.g.f.: exp(25*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(25/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 25/13, 287/169, -9725/2197, -534143/28561..

Mathematica

Table[13^n*HermiteH[n, 25/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 25/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(25*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(25/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A001022 (denominators).

Sequence in context: A078463 A231790 A125413 * A265967 A225873 A351925

Adjacent sequences: A160081 A160082 A160083 * A160085 A160086 A160087

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved