A160303 Numerator of Hermite(n, 5/31).

1, 10, -1822, -56660, 9939052, 534992600, -90164363720, -7071178300400, 1142359566484880, 120150033211799200, -18559035448937462240, -2494873992820155246400, 367426387533234274214080, 61216037645736403345110400, -8568355342448027542061898880

Offset

0,2

Links

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

Formula

a(n+2) = 10*a(n+1) - 1922*(n+1)*a(n). - Bruno Berselli, Mar 28 2018

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

a(n) = 31^n * Hermite(n, 5/31).

E.g.f.: exp(10*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 10/31, -1822/961, -56660/29791, 9939052/923521, ...

Mathematica

Numerator/@HermiteH[Range[0, 20], 5/31] (* Harvey P. Dale, May 14 2011 *)
Table[31^n*HermiteH[n, 5/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 5/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/31)^(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: A211915 A182326 A370310 * A336666 A024138 A261603

Adjacent sequences: A160300 A160301 A160302 * A160304 A160305 A160306

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved