A159650 Numerator of Hermite(n, 12/19).

1, 24, -146, -38160, -599604, 95815584, 4464144456, -307933642944, -29952193511280, 1059772077373824, 220063883293269216, -2370021199600548096, -1804627869905557267776, -22777205204394225722880, 16391584262028099097996416, 623630012494691211958785024

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 24/19, -146/361, -38160/6859, -599604/130321, 95815584/2476099, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Crossrefs

Cf. A001029 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(24/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Maple

A159650 := proc(n)
        orthopoly[H](n,12/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 12/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 12/19], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n,12/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 24*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 19^n * Hermite(n, 12/19).

E.g.f.: exp(24*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/19)^(n-2*k)/(k!*(n-2*k)!)). (End)