A160152 Numerator of Hermite(n, 25/27).

1, 50, 1042, -93700, -9242708, 84323000, 71595491320, 2842116962000, -588597736311920, -62580339060364000, 4594562542866814240, 1142149470643447832000, -16580120530325575181120, -20812053164894042027728000, -726343053712911149403451520

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, 25/27).

E.g.f.: exp(50*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 50/27, 1042/729, -93700/19683, -9242708/531441, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 25/27]] (* Harvey P. Dale, Nov 15 2014 *)
Table[27^n*HermiteH[n, 25/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 25/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(50*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(50/27)^(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: A112890 A231421 A200207 * A318760 A250520 A017766

Adjacent sequences: A160149 A160150 A160151 * A160153 A160154 A160155

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved