A160293 Numerator of Hermite(n, 11/30).

1, 11, -329, -13519, 295441, 27584051, -361317689, -78451432279, 275184965281, 285452190822491, 2025474989659351, -1262254633814956639, -23910902170778310479, 6553155098722204435331, 211963483784997365090791, -38953278800314916926586599, -1859239582352196300555291839

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..412

Formula

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

a(n) = 15^n * Hermite(n, 11/30).

E.g.f.: exp(11*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 11/15, -329/225, -13519/3375, 295441/50625, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 11/30]] (* Harvey P. Dale, Jul 24 2013 *)
Table[15^n*HermiteH[n, 11/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/15)^(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. A001024 (denominators).

Sequence in context: A108274 A295171 A254545 * A084944 A107441 A086923

Adjacent sequences: A160290 A160291 A160292 * A160294 A160295 A160296

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved