A247850 The 5th Hermite Polynomial evaluated at n: H_5(n) = 32*n^5 - 160*n^3 + 120*n.
0, -8, -16, 3816, 23008, 80600, 214992, 483784, 967616, 1774008, 3041200, 4941992, 7687584, 11531416, 16773008, 23761800, 32900992, 44651384, 59535216, 78140008, 101122400, 129211992, 163215184, 204019016, 252595008, 310003000, 377394992, 456018984
Offset: 0
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 (6,-15,20,-15,6,-1).
Crossrefs
Programs
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Mathematica
Table[32 n^5 - 160 n^3 + 120 n, {n, 0, 30}] -
PARI
a(n)=32*n^5-160*n^3+120*n \\ Charles R Greathouse IV, Oct 07 2015
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Python
from sympy import hermite def A247850(n): return hermite(5,n) # Chai Wah Wu, Jan 06 2022
Formula
G.f.: -x*(8-32*x-3792*x^2-32*x^3+8*x^4)/(x-1)^6.
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).