A160088 Numerator of Hermite(n, 2/27).

1, 4, -1442, -17432, 6237580, 126613744, -44965503224, -1287479045408, 453768009722512, 16832227624528960, -5887014913080686624, -268961938417954983296, 93340097422316232142528, 5079118464249805316316928, -1748851732685582642764208000

Offset

0,2

Links

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

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 27^n * Hermite(n, 2/27).

E.g.f.: exp(4*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 4/27, -1442/729, -17432/19683, 6237580/531441...

Mathematica

Numerator[HermiteH[Range[0, 20], 2/27]] (* Harvey P. Dale, Mar 26 2016 *)
Table[27^n*HermiteH[n, 2/27], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 729*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A009971 (denominators).

Sequence in context: A201390 A030271 A301576 * A094546 A203035 A030253

Adjacent sequences: A160085 A160086 A160087 * A160089 A160090 A160091

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved