A159460 Numerator of Hermite(n, 9/11).

1, 18, 82, -7236, -189780, 3588408, 294225144, 85684176, -496875078768, -9109635982560, 918220473870624, 38573287607466432, -1749983724509205312, -143516534253248214144, 2922151180747492056960, 538832739303459806545152, -908419478651119648952064

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) - 18*a(n-1) + 242*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jun 15 2018: (Start)

a(n) = 11^n * Hermite(n,9/11).

E.g.f.: exp(18*x-121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 18/11, 82/121, -7236/1331, -189780/14641, 3588408/161051, ...

Maple

A159460 := proc(n)
        orthopoly[H](n, 9/11) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 9/11], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/11)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A043430 A044205 A044586 * A043181 A039358 A043961

Adjacent sequences: A159457 A159458 A159459 * A159461 A159462 A159463

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved