A160082 Numerator of Hermite(n, 21/26).

1, 21, 103, -12033, -357135, 8768781, 787702551, -1241334297, -1889772255903, -36328649434875, 4985785564324551, 227492331940693071, -13759811757404126127, -1211664945256937744643, 35015649011638037564535, 6468927150200228196505911, -41681870334800058325568319

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