A160139 Numerator of Hermite(n, 11/27).

1, 22, -974, -85580, 2377516, 551407912, -5201117576, -4938141000848, -55556496038000, 56376233721055072, 1969289482873847584, -778641119029758302912, -48713569344985450216256, 12551406492954971362990720, 1199447936209863593384712064

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, 11/27).

E.g.f.: exp(22*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 22/27, -974/729, -85580/19683, 2377516/531441, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 11/27]] (* Harvey P. Dale, Mar 06 2014 *)
Table[27^n*HermiteH[n, 11/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/27)^(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: A211887 A041927 A041924 * A004633 A232277 A223781

Adjacent sequences: A160136 A160137 A160138 * A160140 A160141 A160142

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved