A160284 Numerator of Hermite(n, 22/29).

1, 44, 254, -136840, -7302644, 599343184, 87786336136, -2185972622944, -1129779117074800, -20295833536956736, 16209579598652226016, 1054597422432310244224, -253507355147241835002176, -32440318000852390709512960, 4115817835612084772939010176

Offset

0,2

Links

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

Formula

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 29^n * Hermite(n, 22/29).

E.g.f.: exp(44*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 44/29, 254/841, -136840/24389, -7302644/707281, ...

Mathematica

Table[Numerator[HermiteH[n, 22/29]], {n, 0, 15}] (* Wesley Ivan Hurt, May 24 2014 *)
Table[29^n*HermiteH[n, 22/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 22/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A122245 A031175 A098826 * A060836 A135182 A094794

Adjacent sequences: A160281 A160282 A160283 * A160285 A160286 A160287

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved