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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. 2
0, -10720, 46144, -406944, 27728000, 421271200, 2938887360, 13857016544, 50936525056, 157077960480, 424598062400, 1035360742240, 2323482102144, 4869001213856, 9632766324160, 18144829893600, 32760875409920, 57003614246944, 96008691963456, 157097430355040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

FORMULA

Gf.: -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).

MATHEMATICA

Table[512 n^9 - 9216 n^7 + 48384 n^5 - 80640 n^3 + 30240 n, {n, 0, 30}] (* or *) CoefficientList[Series[- 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, {x, 0, 30}], x]

PROG

(MAGMA) [512*n^9-9216*n^7+48384*n^5-80640*n^3+30240*n: n in [0..30]]; /* or */ I:=[0, -10720, 46144, -406944, 27728000, 421271200, 2938887360, 13857016544, 50936525056, 157077960480]; [n le 10 select I[n] else 10*Self(n-1)-45*Self(n-2)+120*Self(n-3)-210*Self(n-4)+252*Self(n-5)-210*Self(n-6)+120*Self(n-7)-45*Self(n-8)+10*Self(n-9)-Self(n-10): n in [1..30]];

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

CROSSREFS

Cf. similar sequences listed in A247850.

Sequence in context: A207534 A238067 A184603 * A117090 A255038 A255031

Adjacent sequences:  A247851 A247852 A247853 * A247855 A247856 A247857

KEYWORD

sign,easy

AUTHOR

Vincenzo Librandi, Sep 26 2014

STATUS

approved

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Last modified December 10 23:14 EST 2019. Contains 329909 sequences. (Running on oeis4.)