A160083 Numerator of Hermite(n, 23/26).

1, 23, 191, -11155, -450239, 4726063, 869603359, 10416421493, -1817903853055, -69977792337337, 3920574297234559, 326698146936593917, -7062637857576430271, -1487528354699082823585, -3179921411888070331681, 6965845981962634303575557, 176336659143413105563860481

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, 23/26).

E.g.f.: exp(23*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 23/13, 191/169, -11155/2197, -450239/28561

Mathematica

HermiteH[Range[0, 20], 23/26]//Numerator (* Harvey P. Dale, Jul 15 2017 *)
Table[13^n*HermiteH[n, 23/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/13)^(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: A201859 A232150 A269086 * A140545 A062640 A108646

Adjacent sequences: A160080 A160081 A160082 * A160084 A160085 A160086

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved