A159707 Numerator of Hermite(n, 4/21).

1, 8, -818, -20656, 1999180, 88867808, -8105441336, -535131970624, 45761939043472, 4141986697070720, -330122378550514976, -39173301696567870208, 2889460903124553335488, 437725912381470764965376, -29628751416174362424982400, -5642069577415795905192322048

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) - 8*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 17 2014

From G. C. Greubel, May 22 2018: (Start)

a(n) = 21^n * Hermite(n,4/21).

E.g.f.: exp(8*x-441*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/21)^(n-2k)/(k!*(n-2k)!). (End)

Example

Numerator of 1, 8/21, -818/441, -20656/9261, 1999180/194481, 88867808/4084101, ...

Maple

A159707 := proc(n)
        orthopoly[H](n, 4/21) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator[Table[HermiteH[n, 4/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/21)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 22 2018

Crossrefs

Cf. A009965 (denominators).

Sequence in context: A220186 A054945 A158817 * A097818 A360195 A262379

Adjacent sequences: A159704 A159705 A159706 * A159708 A159709 A159710

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved