A159850 Numerator of Hermite(n, 17/22).

1, 17, 47, -7429, -160415, 4464217, 269993839, -1892147821, -489536076223, -4658915114335, 987008017069999, 28053710866880683, -2150502256703365727, -118026514721378720791, 4759029349325350323695, 480777330814562061542723, -9102061914203466628786559

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..435

Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Formula

D-finite with recurrence a(n) = 17*a(n-1) + 242*(1-n)*a(n-2). - Robert Israel, Dec 07 2017

E.g.f.: exp(17*x - 121*x^2). - Simon Plouffe, Jun 23 2018

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

a(n) = 11^n * Hermite(n, 17/22).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 17/11, 47/121, -7429/1331, -160415/14641, ...

Maple

f:= gfun:-rectoproc({a(n) = 17*a(n-1)+242*(1-n)*a(n-2), a(0)=1, a(1)=17}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Dec 07 2017

Mathematica

Numerator[Table[HermiteH[n, 17/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[11^n*HermiteH[n, 17/22], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A147058 A083296 A362480 * A031122 A051869 A297818

Adjacent sequences: A159847 A159848 A159849 * A159851 A159852 A159853

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved