A160297 Numerator of Hermite(n, 23/30).

1, 23, 79, -18883, -540959, 21547343, 1712746639, -18784653403, -5827198941119, -66400823394937, 22072936773448399, 806481251066529677, -90711968254039392479, -6441374025602166282817, 382513411697280621497359, 49378464830331101876186357

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, 23/30).

E.g.f.: exp(23*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 23/15, 79/225, -18883/3375, -540959/50625, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 23/30]] (* Harvey P. Dale, Sep 30 2012 *)
Table[15^n*HermiteH[n, 23/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/15)^(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: A142650 A078597 A280576 * A210706 A304592 A302729

Adjacent sequences: A160294 A160295 A160296 * A160298 A160299 A160300

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved