A160153 Numerator of Hermite(n, 26/27).

1, 52, 1246, -86840, -9965684, -11764688, 72038072584, 3848897264992, -535077911012720, -72717589071528128, 3239977716589449184, 1228701289925531463808, 11929704457466050105024, -20877013136748863885323520, -1311720301397752435727447936

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..376

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 26/27).

E.g.f.: exp(52*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 52/27, 1246/729, -86840/19683, -9965684/531441, ...

Mathematica

Table[27^n*HermiteH[n, 26/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 26/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(52*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(52/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Crossrefs

Cf. A009971 (denominators).

Sequence in context: A331127 A216939 A130000 * A017768 A035721 A035798

Adjacent sequences: A160150 A160151 A160152 * A160154 A160155 A160156

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved