A160146 Numerator of Hermite(n, 17/27).

1, 34, -302, -109412, -2399060, 556522744, 36410920696, -3630489660848, -495046505092208, 25514450230996000, 7363491547673817376, -121641971747011889216, -122231504480991087309632, -2027623214667976954804352, 2247836746633993852403416960

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, 17/27).

E.g.f.: exp(34*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 34/27, -302/729, -109412/19683, -2399060/531441, ...

Mathematica

Table[27^n*HermiteH[n, 17/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/27)^(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: A220565 A230803 A209808 * A101092 A233061 A281805

Adjacent sequences: A160143 A160144 A160145 * A160147 A160148 A160149

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved