A160301 Numerator of Hermite(n, 3/31).

1, 6, -1886, -34380, 10668396, 328323816, -100553342664, -4389550302096, 1326507370388880, 75452769667361376, -22493207874982677984, -1585161480256581714624, 466040432011344287649984, 39356406972705866391987840, -11408347792399213172870573184

Offset

0,2

Links

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

Formula

a(n+2) = 6*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, 3/31).

E.g.f.: exp(6*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 6/31, -1886/961, -34380/29791, 10668396/923521, ...

Mathematica

Table[31^n*HermiteH[n, 3/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 3/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/31)^(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: A357760 A250393 A221627 * A209496 A341872 A024086

Adjacent sequences: A160298 A160299 A160300 * A160302 A160303 A160304

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved