A159874 Numerator of Hermite(n, 10/23).

1, 20, -658, -55480, 978892, 254369200, -90954680, -1616554775200, -31657485143920, 13049369914414400, 562429971828694240, -126813734257930467200, -9081834697300952909120, 1428390476192666153388800, 153479363950530629379812480, -18087732454355158476398656000

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 20/23, -658/529, -55480/12167, 978892/279841,...
		

Links

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

Crossrefs

Cf. A009967 (denominators)

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(20/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018

Mathematica

Numerator[Table[HermiteH[n, 11/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 10/23], {n,0,30}] (* G. C. Greubel, Jul 15 2018 *)

PARI

a(n)=numerator(polhermite(n, 10/23)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(20*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018

Formula

From G. C. Greubel, Jul 15 2018: (Start)

a(n) = 23^n * Hermite(n, 10/23).

E.g.f.: exp(20*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/23)^(n-2*k)/(k!*(n-2*k)!)). (End)