A160295 Numerator of Hermite(n, 17/30).

1, 17, -161, -18037, -89279, 30948857, 727008319, -71202772477, -3500523336959, 196821084188897, 17523077945895199, -587802553769818117, -96731879246268143039, 1529691843170459400137, 591886254924566446580479, 425007721743735371005043

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..412

Formula

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

a(n) = 15^n * Hermite(n, 17/30).

E.g.f.: exp(17*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 17/15, -161/225, -18037/3375, -89279/50625, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 17/30]] (* Harvey P. Dale, Jan 02 2016 *)
Table[15^n*HermiteH[n, 17/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(17*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/15)^(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. A001024 (denominators).

Sequence in context: A126538 A164746 A198859 * A125645 A068518 A155664

Adjacent sequences: A160292 A160293 A160294 * A160296 A160297 A160298

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved