A159279 Numerator of Hermite(n, 9/10).

1, 9, 31, -621, -10239, 32049, 2848191, 16019019, -852695679, -14081868711, 256976237151, 9353720489859, -57153446024319, -6126613308134271, -17989779857401089, 4126721296977379899, 50632826565847235841, -2845681598489278796631

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jun 27 2018: (Start)

a(n) = 5^n * Hermite(n, 9/10).

E.g.f.: exp(9*x - 25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 3/10], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
Table[5^n*HermiteH[n, 9/10], {n, 0, 30}] (* G. C. Greubel, Jun 27 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/10)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 27 2018

Crossrefs

Cf. A159247.

Sequence in context: A145950 A177743 A266710 * A048547 A351713 A141573

Adjacent sequences: A159276 A159277 A159278 * A159280 A159281 A159282

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved