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A247850
The 5th Hermite Polynomial evaluated at n: H_5(n) = 32*n^5 - 160*n^3 + 120*n.
6
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
0,2
LINKS
Eric Weisstein's World of Mathematics, Hermite Polynomial.
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).
MATHEMATICA
Table[32 n^5 - 160 n^3 + 120 n, {n, 0, 30}]
PROG
(PARI) a(n)=32*n^5-160*n^3+120*n \\ Charles R Greathouse IV, Oct 07 2015
(Python)
from sympy import hermite
def A247850(n): return hermite(5, n) # Chai Wah Wu, Jan 06 2022
CROSSREFS
Cf. Hermite_k(n): A005843 (k=1), A060626 (k=2), A163322 (k=3), A163323 (k=4), this sequence (k=5), A247851 (k=6), A247852 (k=7), A247853 (k=8), A247854 (k=9), A247855 (k=10).
Sequence in context: A284438 A375103 A236285 * A024280 A115434 A024107
KEYWORD
sign,easy
AUTHOR
Vincenzo Librandi, Sep 25 2014
STATUS
approved