A160251 Numerator of Hermite(n, 8/29).

1, 16, -1426, -76640, 5969356, 611143616, -40423986104, -6814445150336, 366920889983120, 97565908182651136, -3993393901642052384, -1704952878058464945664, 46606527919245814078144, 35158473337439989488532480, -456562766083189138816177024

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 29^n * Hermite(n, 8/29).

E.g.f.: exp(16*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 16/29, -1426/841, -76640/24389, 5969356/707281, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 8/29]] (* Harvey P. Dale, Jul 22 2014 *)
Table[29^n*HermiteH[n, 8/29], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Exp[ 16 x - 841 x^2], {x, 0, n}]]; (* Michael Somos, Jul 30 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/29)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018
(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(16/29)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 12 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A221607 A351760 A330335 * A106176 A263975 A193128

Adjacent sequences: A160248 A160249 A160250 * A160252 A160253 A160254

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved