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A160082 Numerator of Hermite(n, 21/26). 1
1, 21, 103, -12033, -357135, 8768781, 787702551, -1241334297, -1889772255903, -36328649434875, 4985785564324551, 227492331940693071, -13759811757404126127, -1211664945256937744643, 35015649011638037564535, 6468927150200228196505911, -41681870334800058325568319 (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, 21/26).

E.g.f.: exp(21*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(21/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 21/13, 103/169, -12033/2197, -357135/28561

MATHEMATICA

Table[13^n*HermiteH[n, 21/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 21/26)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(21*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(21/13)^(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: A305481 A219385 A219297 * A201468 A306259 A069499

Adjacent sequences:  A160079 A160080 A160081 * A160083 A160084 A160085

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified September 25 03:11 EDT 2021. Contains 347651 sequences. (Running on oeis4.)