A159865 Numerator of Hermite(n, 3/23).

1, 6, -1022, -18828, 3130860, 98465256, -15971457864, -720886192272, 113959299787152, 6785336530113120, -1044408433392582624, -78055311088952305344, 11686493481289162746048, 1061109190473073445123712, -154369376198812703738401920, -16643365586480040091602833664

Offset

0,2

Links

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

Formula

From _G. C. Greubel_, Jul 14 2018: (Start)

a(n) = 23^n * Hermite(n, 3/23).

E.g.f.: exp(6*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 3/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
Table[23^n*HermiteH[n, 3/23], {n, 0, 30}] (* _G. C. Greubel_, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 529*x^2))) \\ _G. C. Greubel_, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018

Crossrefs

Cf. A159858, A159859.

Sequence in context: A080474 A079190 A203303 * A370680 A004806 A282233

Adjacent sequences: A159862 A159863 A159864 * A159866 A159867 A159868

Keyword

sign,frac

Author

_N. J. A. Sloane_, Nov 12 2009

Status

approved