A160193 Numerator of Hermite(n, 5/28).

1, 5, -367, -5755, 402817, 11037925, -734331695, -29632858075, 1866841880705, 102262852326725, -6074903893493615, -431244900588230075, 24038761085803317505, 2148769817796050860325, -111757677404273451703855, -12351237147086094379982875, 595378957401697424118753025

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 5/14, -367/196, -5755/2744, 402817/38416, 11037925/537824,..
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..417
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Crossrefs

Cf. A001023 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(5/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Maple

A160193 := proc(n)
        orthopoly[H](n,5/28) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator/@HermiteH[Range[0,20],5/28] (* Harvey P. Dale, Jul 11 2011 *)
Table[14^n*HermiteH[n, 5/28], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,5/28)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -5*a(n-1) +392*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 09 2018: (Start)

a(n) = 14^n * Hermite(n, 5/28).

E.g.f.: exp(5*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/14)^(n-2*k)/(k!*(n-2*k)!)). (End)