A160299 Numerator of Hermite(n, 1/31).

1, 2, -1918, -11524, 11036140, 110668792, -105835967816, -1487904444976, 1420941302106512, 25719901350164000, -24528002841138116576, -543392509632428313152, 517484251048077204023488, 13567773344258481022584704, -12902725949998740057685701760

Offset

0,2

Links

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

Formula

a(n+2) = 2*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, 1/31).

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

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

Example

Numerators of 1, 2/31, -1918/961, -11524/29791, 11036140/923521, ...

Mathematica

Table[31^n*HermiteH[n, 1/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 1/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/31)^(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: A069793 A230082 A217372 * A232963 A238119 A177188

Adjacent sequences: A160296 A160297 A160298 * A160300 A160301 A160302

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved