A159620 Numerator of Hermite(n, 3/19).

1, 6, -686, -12780, 1409196, 45363816, -4815014664, -225406138896, 22982647278480, 1439841741934176, -140702191563957984, -11239870526148498624, 1050017582244063317184, 103682343732014971981440, -9233370964550688463200384, -1103421356230511467567597824

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..396

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 19^n * Hermite(n, 3/19).

E.g.f.: exp(6*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 3/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 3/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/19)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(6*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A159564, A159618.

Sequence in context: A331724 A046985 A159371 * A125535 A364688 A116298

Adjacent sequences: A159617 A159618 A159619 * A159621 A159622 A159623

Keyword

sign,frac,easy

Author

N. J. A. Sloane, Nov 12 2009

Status

approved