A160150 Numerator of Hermite(n, 22/27).

1, 44, 478, -107272, -6810740, 325937744, 63991555336, -35674949728, -654667511547248, -28389257894451520, 7341419739167121376, 736937848624456502144, -85316424437286206533952, -16647387274774084049005312, 884602468694263060488292480

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..375

Formula

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

a(n) = 27^n * Hermite(n, 22/27).

E.g.f.: exp(44*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 44/27, 478/729, -107272/19683, -6810740/531441, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 22/27]] (* Harvey P. Dale, Jul 29 2013 *)
Table[27^n*HermiteH[n, 22/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 22/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/27)^(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: A231242 A221730 A306036 * A210119 A272186 A222514

Adjacent sequences: A160147 A160148 A160149 * A160151 A160152 A160153

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved