A160270 Numerator of Hermite(n, 16/29).

1, 32, -658, -128704, -798260, 840376192, 33605404744, -7405703577856, -632652549947248, 79406265745318400, 12118094804951629024, -947834356077803359232, -254539689475704747697472, 10985818579851831076419584, 5917311044631018607598349440

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..371

Formula

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 29^n * Hermite(n, 16/29).

E.g.f.: exp(32*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 32/29, -658/841, -128704/24389, -798260/707281, ...

Mathematica

Numerator/@HermiteH[Range[0, 20], 16/29] (* Harvey P. Dale, Jun 07 2011 *)
Table[29^n*HermiteH[n, 16/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 16/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A028152 A028176 A028151 * A028102 A028143 A028101

Adjacent sequences: A160267 A160268 A160269 * A160271 A160272 A160273

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved