A159651 Numerator of Hermite(n, 13/19).

1, 26, -46, -38740, -907604, 88283416, 5571819256, -237576457456, -34336962413680, 479480595510176, 235588077247357216, 2663440108847816896, -1801791066668467770176, -69922612836437647611520, 15093623018002859652972416, 1099211969018786093034526976

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) -26*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, 13/19).

E.g.f.: exp(26*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 26/19, -46/361, -38740/6859, -907604/130321, 88283416/2476099,..

Maple

A159651 := proc(n)
        orthopoly[H](n, 13/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 13/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 13/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/19)^(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: A304673 A039458 A291672 * A118367 A316120 A261932

Adjacent sequences: A159648 A159649 A159650 * A159652 A159653 A159654

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved