A159656 Numerator of Hermite(n, 18/19).

1, 36, 574, -31320, -2370804, 5103216, 8742318216, 292616324064, -33649488597360, -2901533477298624, 114199171722894816, 25060241888120278656, -4801113850900597056, -217294775817306515769600, -7777548674818481563737984, 1916423841667868925104549376

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) -36*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 19^n * Hermite(n, 18/19).

E.g.f.: exp(36*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 36/19, 574/361, -31320/6859, -2370804/130321, 5103216/2476099,...

Maple

A159656 := proc(n)
        orthopoly[H](n, 18/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 18/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 18/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 18/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Crossrefs

Cf. A001029 (denominators).

Sequence in context: A329913 A200708 A186309 * A081447 A218311 A183356

Adjacent sequences: A159653 A159654 A159655 * A159657 A159658 A159659

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved