A159561 Numerator of Hermite(n, 11/18).

1, 11, -41, -4015, -24239, 2335091, 45319591, -1771192951, -70875538655, 1515835139291, 120010721891191, -1135534984848319, -226349991243433871, -282369893132640445, 473587012734212687431, 5849872057701168091001, -1086467848309423981456319

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 9^n * Hermite(n, 11/18).

E.g.f.: exp(11*x - 81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 11/18], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[9^n*HermiteH[n, 11/18], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/18)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 81*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A159545, A159546.

Sequence in context: A050526 A257967 A104118 * A020452 A249413 A003356

Adjacent sequences: A159558 A159559 A159560 * A159562 A159563 A159564

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved