A159470 Numerator of Hermite(n, 10/11).

1, 20, 158, -6520, -245108, 1409200, 324764680, 4449135200, -461168663920, -17836899025600, 647687369505760, 56119043032067200, -601762916982989120, -175004959304782931200, -1606953049267174852480, 560777741139261073856000, 17048794391625066191622400

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) - 20*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,10/11).

E.g.f.: exp(20*x-121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 20/11, 158/121, -6520/1331, -245108/14641, 1409200/161051, ...

Maple

A159470 := proc(n)
        orthopoly[H](n, 10/11) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 10/11], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 10/11)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/11)^(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: A120693 A120692 A324948 * A059601 A125357 A126515

Adjacent sequences: A159467 A159468 A159469 * A159471 A159472 A159473

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved