A160107 Numerator of Hermite(n, 7/27).

1, 14, -1262, -58492, 4701100, 406940744, -28573848584, -3959951508688, 236185377526672, 49495469682710240, -2406287948347046624, -755331979250773951936, 28017398406079098428608, 13607531886656648441072768, -340536322975630153440817280

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, 7/27).

E.g.f.: exp(14*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 14/27, -1262/729, -58492/19683, 4701100/531441, ...

Mathematica

HermiteH[Range[0, 20], 7/27]//Numerator (* Harvey P. Dale, Jun 08 2018 *)
Table[27^n*HermiteH[n, 7/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/27)^(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: A204972 A209677 A137603 * A322256 A054004 A280087

Adjacent sequences: A160104 A160105 A160106 * A160108 A160109 A160110

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved