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A247854
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The 9th Hermite Polynomial evaluated at n: H_9(n) = 512*n^9 - 9216*n^7 + 48384*n^5 - 80640*n^3 + 30240*n.
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2
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0, -10720, 46144, -406944, 27728000, 421271200, 2938887360, 13857016544, 50936525056, 157077960480, 424598062400, 1035360742240, 2323482102144, 4869001213856, 9632766324160, 18144829893600, 32760875409920, 57003614246944, 96008691963456, 157097430355040
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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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).
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MATHEMATICA
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Table[512 n^9 - 9216 n^7 + 48384 n^5 - 80640 n^3 + 30240 n, {n, 0, 30}]
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PROG
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(Python)
from sympy import hermite
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CROSSREFS
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Cf. similar sequences listed in A247850.
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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