A159005 Numerator of Hermite(n, 5/7).

1, 10, 2, -1940, -19988, 560600, 15400120, -175631600, -12320798320, 14487191200, 11011816030240, 95920712926400, -10911530551334720, -221918063914793600, 11682109283252497280, 421292676523621792000, -12959773881144953081600

Offset

0,2

Links

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

Formula

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

a(n) = 7^n * Hermite(n, 5/7).

E.g.f.: exp(10*x - 49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 5/7], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[7^n*HermiteH[n, 5/7], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/7)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 49*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/7)^(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. A158980.

Sequence in context: A290308 A354941 A352689 * A144859 A280519 A010172

Adjacent sequences: A159002 A159003 A159004 * A159006 A159007 A159008

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved