A159870 Numerator of Hermite(n, 6/23).

1, 12, -914, -36360, 2464716, 183452112, -10836922296, -1294597074528, 64723081629840, 11734146618363072, -475483423858979616, -129853072308589057152, 3975439219167736085184, 1696319876659859502624000, -34322352500514728084132736, -25537758243092015689876280832

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 12/23, -914/529, -36360/12167, 2464716/279841
		

Links

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

Crossrefs

Cf. A009967 (denominators)

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(12/23)^(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

Mathematica

Numerator[Table[HermiteH[n, 6/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 6/23], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)

PARI

a(n)=numerator(polhermite(n, 6/23)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(12*x - 529*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 23^n * Hermite(n, 6/23).

E.g.f.: exp(12*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/23)^(n-2*k)/(k!*(n-2*k)!)). (End)