A159520 Numerator of Hermite(n, 14/15).

1, 28, 334, -15848, -894644, 3476368, 2110287304, 49701850912, -5255753182064, -326087752380992, 12155343320691424, 1807744498693823872, -9552103473995480384, -10029279190218522359552, -224940012003245065821056, 56886138562285829022188032

Offset

0,2

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)

Formula

D-finite with recurrence a(n) -28*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,14/15).

E.g.f.: exp(28*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 28/15, 334/225, -15848/3375, -894644/50625, 3476368/759375

Maple

A159520 := proc(n)
        orthopoly[H](n, 14/15) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 14/15], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 14/15)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/15)^(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

Crossrefs

Cf. A001024 (denominators).

Sequence in context: A125416 A241038 A055753 * A027820 A092713 A134288

Adjacent sequences: A159517 A159518 A159519 * A159521 A159522 A159523

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved