A160260 Numerator of Hermite(n, 12/29).

1, 24, -1106, -107280, 3006156, 793927584, -6227509944, -8161777416384, -122559955912560, 106883437972961664, 4420515123955413216, -1691687063730285271296, -122388860352949901833536, 31207679045861280271833600, 3425139117578273280016104576

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..372

Formula

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

a(n) = 29^n * Hermite(n, 12/29).

E.g.f.: exp(24*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 24/29, -1106/841, -107280/24389, 3006156/707281,...

Mathematica

Table[29^n*HermiteH[n, 12/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0, 20], 12/29]//Numerator (* Harvey P. Dale, Dec 27 2019 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 12/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/29)^(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: A046906 A130552 A374885 * A268149 A114051 A269092

Adjacent sequences: A160257 A160258 A160259 * A160261 A160262 A160263

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved