A159252 Numerator of Hermite(n, 7/10).

1, 7, -1, -707, -4799, 107807, 1954399, -18661307, -814668799, 1761841207, 378933847999, 1771616332493, -196012302071999, -2435055913999793, 110362604948800799, 2477077374441460693, -65432412090510374399, -2439688784186741175193

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A159247.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(7/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018

Mathematica

Numerator[Table[HermiteH[n,7/10],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

a(n)=numerator(polhermite(n,7/10)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)

a(n) = 5^n * Hermite(n, 7/10).

E.g.f.: exp(7*x-25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/5)^(n-2*k)/(k!*(n-2*k)!)). (End)