A247854 The 9th Hermite Polynomial evaluated at n: H_9(n) = 512*n^9 - 9216*n^7 + 48384*n^5 - 80640*n^3 + 30240*n.

0, -10720, 46144, -406944, 27728000, 421271200, 2938887360, 13857016544, 50936525056, 157077960480, 424598062400, 1035360742240, 2323482102144, 4869001213856, 9632766324160, 18144829893600, 32760875409920, 57003614246944, 96008691963456, 157097430355040

Offset: 0

Author

Vincenzo Librandi, Sep 26 2014

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Hermite Polynomial.
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. similar sequences listed in A247850.

Programs

Mathematica

Table[512 n^9 - 9216 n^7 + 48384 n^5 - 80640 n^3 + 30240 n, {n, 0, 30}]

PARI

a(n)=polhermite(9,n) \\ Charles R Greathouse IV, Jan 29 2016

Python

from sympy import hermite
def A247854(n): return hermite(9,n) # Chai Wah Wu, Jan 06 2022

Formula

G.f.: -x*(10720-153344*x+1350784*x^2-35160320*x^3-117890240* x^4-35160320*x^5+1350784*x^6-153344*x^7+10720*x^8)/(x-1)^10.

a(n) = 10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10).