A159030 Numerator of Hermite(n, 1/9).

1, 2, -158, -964, 74860, 774392, -59087816, -870884656, 65263814032, 1259194142240, -92636252574176, -2225167015577152, 160627468056027328, 4646979614394038144, -328987488497205476480, -11197324742440089463552, 777044947563329128919296

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 9^n * Hermite(n, 1/9).

E.g.f.: exp(2*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/9)^(n-2k)/(k!*(n-2k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 1/9], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/9)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) for(n=0, 30, print1(9^n*polhermite(n, 1/9), ", ")) \\ G. C. Greubel, Jun 10 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Crossrefs

Cf. A158811, A158954, A158960, A158980.

Sequence in context: A233575 A233263 A124225 * A064071 A116638 A326488

Adjacent sequences: A159027 A159028 A159029 * A159031 A159032 A159033

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved