A159873 Numerator of Hermite(n, 9/23).

1, 18, -734, -51300, 1406316, 242415288, -3075936456, -1594219104432, -5915558486640, 13386990447152928, 297293775958538784, -136283070963624280128, -5913000241950711410496, 1623815864599061055116160, 110556090890573183732052864, -22061950950410975041203610368

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, 9/23).

E.g.f.: exp(18*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 18/23, -734/529, -51300/12167, 1406316/279841,...

Mathematica

HermiteH[Range[0, 20], 9/23]//Numerator (* Harvey P. Dale, Aug 11 2016 *)
Table[23^n*HermiteH[n, 9/23], {n, 0, 30}] (* G. C. Greubel, Jul 15 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/23)^(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: A073421 A346216 A295439 * A259458 A180781 A264468

Adjacent sequences: A159870 A159871 A159872 * A159874 A159875 A159876

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved