A160131 Numerator of Hermite(n, 8/27).

1, 16, -1202, -65888, 4203340, 451512256, -23418152504, -4324519655552, 169813349966992, 53158210861830400, -1377759404477582624, -797090864837128553984, 9343051491617413259968, 14095390595056279792663552, 48438051548784025753183360, -286940104001508238715797489664

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, 8/27).

E.g.f.: exp(16*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 16/27, -1202/729, -65888/19683, 4203340/531441, ...

Mathematica

Table[27^n*HermiteH[n, 8/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/27)^(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: A254333 A102807 A373453 * A206691 A064346 A222888

Adjacent sequences: A160128 A160129 A160130 * A160132 A160133 A160134

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved