A160317 Numerator of Hermite(n, 19/31).

1, 38, -478, -164236, -3484820, 1130223208, 76437602104, -10129105154704, -1413297494585968, 102039816064461920, 28324733071797627424, -884865408030648260288, -632466392109110072889152, -3625187129327311294505344, 15665048162323786452017148800

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..368

Formula

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 19/31).

a(n+2) = 38*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(38*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 38/31, -478/961, -164236/29791, -3484820/923521, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 19/31]] (* Harvey P. Dale, Dec 26 2017 *)
Table[31^n*HermiteH[n, 19/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Crossrefs

Cf. A009975 (denominators).

Sequence in context: A254471 A039685 A006418 * A088891 A159784 A243820

Adjacent sequences: A160314 A160315 A160316 * A160318 A160319 A160320

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved