A159904 Numerator of Hermite(n, 17/23).

1, 34, 98, -68612, -2643860, 200474744, 20802160696, -565340211248, -173282369297008, -1106561008095200, 1612371646170873376, 66528051435456910784, -16502827469331089383232, -1405736274981817978343552, 179184855663797992113292160, 26914050797599819627076625664

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 23^n * Hermite(n, 17/23).

E.g.f.: exp(34*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 34/23, 98/529, -68612/12167, -2643860/279841, ...

Mathematica

HermiteH[Range[0, 20], 17/23]//Numerator (* Harvey P. Dale, Apr 08 2018 *)
Table[23^n*HermiteH[n, 17/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A009967 (denominators).

Sequence in context: A233028 A044221 A044602 * A282854 A165222 A173308

Adjacent sequences: A159901 A159902 A159903 * A159905 A159906 A159907

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved