A159307 Numerator of Hermite(n, 3/11).

1, 6, -206, -4140, 124716, 4755816, -122371464, -7639673616, 161459218320, 15759163430496, -257103196917984, -39679794683308224, 446329942095824064, 117908103412902026880, -696705377356050344064, -403652886627048369133824, 107123200040172534149376

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

Formula

From G. C. Greubel, Jun 26 2018: (Start)

a(n) = 11^n * Hermite(n,6/11).

E.g.f.: exp(6*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

a(n) = 6*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]

Mathematica

Numerator[Table[HermiteH[n, 3/11], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/11)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018
(Magma) I:=[1, 6]; [n le 2 select I[n] else 6*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jan 27 2018

Crossrefs

Cf. A159280.

Sequence in context: A054653 A061540 A173370 * A284768 A024083 A172530

Adjacent sequences: A159304 A159305 A159306 * A159308 A159309 A159310

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved