A160279 Numerator of Hermite(n, 17/29).

1, 34, -526, -132260, -1842644, 827195384, 43621279096, -6864932326064, -747004639162480, 66976371647992864, 13585352863673379616, -664640573754345065536, -273953978191332601883456, 4100670082152392338741120, 6129700469924860012300846976

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, 17/29).

E.g.f.: exp(34*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 34/29, -526/841, -132260/24389, -1842644/707281, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 17/29]] (* Harvey P. Dale, Dec 24 2015 *)
Table[29^n*HermiteH[n, 17/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/29)^(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: A066291 A228682 A020929 * A230332 A232320 A133720

Adjacent sequences: A160276 A160277 A160278 * A160280 A160281 A160282

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved