A159875 Numerator of Hermite(n, 11/23).

1, 22, -574, -59180, 519916, 261887912, 3011178424, -1596218540048, -57417595289200, 12247206626603872, 816168888129047584, -111619730570629918912, -11954207592599713998656, 1154131532287523742536320, 189809064938941988673313664, -12919196827586077923635071232

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

From G. C. Greubel, Jul 15 2018: (Start)

a(n) = 23^n * Hermite(n, 11/23).

E.g.f.: exp(22*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 22/23, -574/529, -59180/12167, 519916/279841,..

Mathematica

Numerator[HermiteH[Range[0, 20], 11/23]] (* Harvey P. Dale, Nov 20 2012 *)
Table[23^n*HermiteH[n, 11/23], {n, 0, 30}] (* G. C. Greubel, Jul 15 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018

Crossrefs

Cf. A009967 (denominators)

Sequence in context: A223883 A223890 A240369 * A240337 A084271 A092086

Adjacent sequences: A159872 A159873 A159874 * A159876 A159877 A159878

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved