A160269 Numerator of Hermite(n, 15/29).

1, 30, -782, -124380, 214572, 843265800, 23493423480, -7805435749200, -510774640529520, 89706704225349600, 10423307635096361760, -1196167536017489419200, -228737063945077567859520, 17281333628624679401347200, 5520004649081806480856680320

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..372

Formula

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

a(n) = 29^n * Hermite(n, 15/29).

E.g.f.: exp(30*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 30/29, -782/841, -124380/24389, 214572/707281,...

Mathematica

Numerator[HermiteH[Range[0, 20], 15/29]] (* Harvey P. Dale, Dec 12 2012 *)
Table[29^n*HermiteH[n, 15/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 15/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(30*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(30/29)^(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: A045689 A096722 A261030 * A367275 A367332 A049394

Adjacent sequences: A160266 A160267 A160268 * A160270 A160271 A160272

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved