A159524 Numerator of Hermite(n, 7/16).

1, 7, -79, -2345, 13921, 1298087, 177169, -995690633, -7128577855, 969687163207, 14999931831409, -1136200046085097, -29073304341219551, 1541690140398172135, 59169809406576537809, -2348520065747488701257, -130045674520859373502079, 3899449373004841245659783

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) -7*a(n-1) +128*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

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

a(n) = 16^n * Hermite(n,7/16).

E.g.f.: exp(14*x-252*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/8)^(n-2k)/(k!*(n-2k)!). (End)

Example

Numerator of 1, 7/8, -79/64, -2345/512, 13921/4096, 1298087/32768, 177169/262144,.

Maple

A159524 := proc(n)
        orthopoly[H](n, 7/16) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 7/16], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/16)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Crossrefs

Cf. A001018 (denominators).

Sequence in context: A235370 A098105 A201301 * A113034 A267798 A201704

Adjacent sequences: A159521 A159522 A159523 * A159525 A159526 A159527

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved