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A160084 Numerator of Hermite(n, 25/26). 1
1, 25, 287, -9725, -534143, -205375, 897567295, 22855682875, -1552252148095, -100608070196375, 2206749279595615, 395224009253637875, 1675906409804450305, -1561130921287643963375, -46392205796871853724545, 6227466374611334891576875, 390895142755423670672865025 (list; graph; refs; listen; history; text; internal format)
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 A029987

Adjacent sequences:  A160081 A160082 A160083 * A160085 A160086 A160087

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)