A160252 Numerator of Hermite(n, 9/29).

1, 18, -1358, -84996, 5322540, 667658808, -32744702856, -7327417341744, 253642619275152, 103163294897460000, -1982702662432970976, -1770895268099070677568, 4807849834551556801728, 35830291388333570578463616, 539816800507699929385760640

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..371

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 29^n * Hermite(n, 9/29).

E.g.f.: exp(18*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 18/29, -1358/841, -84996/24389, 5322540/707281,...

Mathematica

Table[29^n*HermiteH[n, 9/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0, 20], 9/29]//Numerator (* Harvey P. Dale, Feb 17 2021 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A182286 A292609 A275047 * A276015 A210823 A258336

Adjacent sequences: A160249 A160250 A160251 * A160253 A160254 A160255

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved