A159519 Numerator of Hermite(n, 13/15).

1, 26, 226, -17524, -760724, 11764376, 2017502776, 20691256976, -5817161063024, -225734712752224, 17690399773689376, 1475756601500931776, -49197807240738185024, -9248228636364224401024, 47353227812848547963776, 59495024332228675973509376

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 26/15, 226/225, -17524/3375, -760724/50625, 11764376/759375, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Crossrefs

Cf. A001024 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(26/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018

Maple

A159519 := proc(n)
        orthopoly[H](n,13/15) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,13/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,13/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -26*a(n-1) + 450*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jun 11 2018: (Start)

a(n) = 15^n * Hermite(n,13/15).

E.g.f.: exp(26*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/15)^(n-2*k)/(k!*(n-2*k)!)). (End)