A160103 Numerator of Hermite(n, 4/27).

1, 8, -1394, -34480, 5821516, 247659488, -40457575736, -2490185806912, 392988531506320, 32189435503872128, -4899280026394954016, -508516209857615258368, 74506523384461350441664, 9493051794744527363939840, -1336252229871124217359780736

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, 4/27).

E.g.f.: exp(8*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 8/27, -1394/729, -34480/19683, 5821516/531441, ...

Mathematica

Table[27^n*HermiteH[n, 4/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/27)^(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: A123268 A088080 A230472 * A283902 A064073 A282889

Adjacent sequences: A160100 A160101 A160102 * A160104 A160105 A160106

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved