A160226 Numerator of Hermite(n, 3/29).

1, 6, -1646, -30060, 8125356, 250995816, -66828269064, -2934019389456, 769231923622800, 44095556446256736, -11380059521124405984, -809967616552784735424, 205694055560527051103424, 17582550705864569406418560, -4392210914651297082988957824

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..371

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 29^n * Hermite(n, 3/29).

E.g.f.: exp(6*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 6/29, -1646/841, -30060/24389, 8125356/707281

Mathematica

HermiteH[Range[0, 20], 3/29]//Numerator (* Harvey P. Dale, Mar 31 2018 *)
Table[29^n*HermiteH[n, 3/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A281255 A216934 A308029 * A209609 A350595 A034841

Adjacent sequences: A160223 A160224 A160225 * A160227 A160228 A160229

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved