A159523 Numerator of Hermite(n, 5/16).

1, 5, -103, -1795, 30577, 1071925, -14209655, -894286675, 8260417505, 957051642725, -4730742752135, -1248679816448675, 417486712762705, 1920059631628978325, 8905600268107750505, -3396218858538590405875, -34079846807459832998975

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) -5*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,5/16).

E.g.f.: exp(10*x-252*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/8)^(n-2k)/(k!*(n-2k)!). (End)

Example

Numerator of 1, 5/8, -103/64, -1795/512, 30577/4096, 1071925/32768, -14209655/262144,..

Maple

A159523 := proc(n)
        orthopoly[H](n, 5/16) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 5/16], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/16)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/8)^(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: A052138 A308459 A142418 * A172116 A007619 A163212

Adjacent sequences: A159520 A159521 A159522 * A159524 A159525 A159526

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved