A159709 Numerator of Hermite(n, 5/21).

1, 10, -782, -25460, 1814572, 107968600, -6922576520, -640595596400, 36334031470480, 4883382842903200, -239585713383638240, -45467293808242606400, 1869787653165632140480, 499923714198096067542400, -16439748089216177447319680, -6337455503810252016486752000

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) - 10*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,5/21).

E.g.f.: exp(10*x-441*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/21)^(n-2k)/(k!*(n-2k)!). (End)

Example

Numerator of 1, 10/21, -782/441, -25460/9261, 1814572/194481, 107968600/4084101, ...

Maple

A159709 := proc(n)
        orthopoly[H](n, 5/21) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator[Table[HermiteH[n, 5/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/21)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/21)^(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: A108247 A108243 A323494 * A222689 A242373 A221045

Adjacent sequences: A159706 A159707 A159708 * A159710 A159711 A159712

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved