A158965 Numerator of Hermite(n, 3/5).

1, 6, -14, -684, -2004, 124776, 1249656, -29934864, -616988784, 8272012896, 327277030176, -2172344266944, -193036432198464, 145187966975616, 126344808730855296, 656437275502200576, -90819982895128268544, -1070069717772530072064, 70776567154223847830016

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

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

a(n) = 5^n * Hermite(n, 3/5).

E.g.f.: exp(6*x - 25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 3/5], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[5^n*HermiteH[n, 3/5], {n, 0, 30}] (* G. C. Greubel, Jul 13 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/5)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 25*x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 2018

Crossrefs

Cf. A158960, A158961.

Sequence in context: A077401 A364530 A263695 * A284075 A281693 A013314

Adjacent sequences: A158962 A158963 A158964 * A158966 A158967 A158968

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved