A159670 Numerator of Hermite(n, 13/20).

1, 13, -31, -5603, -54239, 3777293, 103343809, -3189282083, -186141999679, 2683005336973, 369934668802849, -556859979508963, -821095451099884319, -9337776913476984947, 2013457072984498425089, 52320717306534037377757, -5360201893968552789356159

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) -13*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 17 2014

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

a(n) = 10^n * Hermite(n, 13/20).

E.g.f.: exp(13*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 13/10, -31/100, -5603/1000, -54239/10000, 3777293/100000,...

Maple

A159670 := proc(n)
        orthopoly[H](n, 13/20) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator[Table[HermiteH[n, 13/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[10^n*HermiteH[n, 13/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/10)^(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. A011557 (denominators).

Sequence in context: A180757 A214488 A247836 * A238736 A087511 A299449

Adjacent sequences: A159667 A159668 A159669 * A159671 A159672 A159673

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved