A160261 Numerator of Hermite(n, 13/29).

1, 26, -1006, -113620, 2122156, 819611416, 3462564856, -8181491724016, -253487023438960, 103499490028946336, 6528273301571581216, -1571126316446016259904, -161635396853273818415936, 27509093252961272911088000, 4249556012170678409171144576

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) +1682*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 29^n * Hermite(n, 13/29).

E.g.f.: exp(26*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 26/29, -1006/841, -113620/24389, 2122156/707281, 819611416/20511149,...

Maple

A160261 := proc(n)
        orthopoly[H](n, 13/29) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[HermiteH[Range[0, 20], 13/29]] (* Harvey P. Dale, May 15 2012 *)
Table[29^n*HermiteH[n, 13/29], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/29)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A263945 A335609 A241871 * A357376 A241874 A330497

Adjacent sequences: A160258 A160259 A160260 * A160262 A160263 A160264

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved