A159857 Numerator of Hermite(n, 21/22).

1, 21, 199, -5985, -270159, 120141, 329415351, 6743277639, -416420774175, -21799821766779, 449168189050791, 62188100645671791, 110264394305901969, -178278691994606939715, -4090744316373113328489, 518102577833892931856151, 25729556002946152951394241

Offset

0,2

Links

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

Formula

a(n) = 21*a(n-1) + 242*(1-n)*a(n-2). - Robert Israel, Dec 07 2017

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

a(n) = 11^n * Hermite(n, 21/22).

E.g.f.: exp(21*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(21/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 21/11, 199/121, -5985/1331, -270159/14641

Maple

f:= gfun:-rectoproc({a(n) = 21*a(n-1)+242*(1-n)*a(n-2), a(0)=1, a(1)=21}, a(n), remember): map(f, [$0..40]); # Robert Israel, Dec 07 2017

Mathematica

Numerator[Table[HermiteH[n, 21/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[11^n*HermiteH[n, 21/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 21/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(21/22)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Crossrefs

Cf. A001020 (denominators), A159850

Sequence in context: A200825 A058086 A270957 * A221126 A239418 A337897

Adjacent sequences: A159854 A159855 A159856 * A159858 A159859 A159860

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved