A159884 Numerator of Hermite(n, 15/23).

1, 30, -158, -68220, -1545108, 242353800, 15444235320, -1075134862800, -146634052663920, 4700919898821600, 1537277046430494240, -3617421136617700800, -17999352900456622989120, -494053808263200360316800, 232741485544984381782852480, 14300169574344055190498016000

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 30/23, -158/529, -68220/12167, -1545108/279841, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
• Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Crossrefs

Cf. A009967 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(30/23)^(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

Mathematica

Numerator[HermiteH[Range[0,20],15/23 ]] (* Harvey P. Dale, Nov 16 2014 *)
Table[23^n*HermiteH[n, 15/23], {n,0,30}] (* G. C. Greubel, Jul 16 2018 *)

PARI

a(n)=numerator(polhermite(n, 15/23)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(30*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018

Formula

E.g.f.: exp(-x*(529*x-30)). - Simon Plouffe, Jun 22 2018

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 23^n * Hermite(n, 15/23).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -30*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021