A160104 Numerator of Hermite(n, 5/27).

1, 10, -1358, -42740, 5512492, 304384600, -37142220680, -3034178687600, 348731717384080, 38877977386007200, -4187277821653825760, -608713688504523233600, 61068424818638825202880, 11260738942261526747094400, -1044883534589865025424443520

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 10/27, -1358/729, -42740/19683, 5512492/531441..
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..376

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(10/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

Mathematica

Numerator[Table[HermiteH[n, 5/27], {n, 0, 30}]] (* or *) Table[27^n* HermiteH[n, 5/27], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)

PARI

a(n)=numerator(polhermite(n,5/27)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 27^n * Hermite(n, 5/27).

E.g.f.: exp(10*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/27)^(n-2*k)/(k!*(n-2*k)!)). (End)