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A247851
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The 6th Hermite Polynomial evaluated at n: H_6(n) = 64*n^6-480*n^4+720*n^2-120.
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2
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-120, 184, -824, 14136, 150664, 717880, 2389704, 6412216, 14857096, 30921144, 59271880, 106439224, 181253256, 295328056, 463591624, 704861880, 1042468744, 1504922296, 2126627016, 2948642104, 4019487880, 5395998264, 7144219336, 9340353976, 12071752584
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (-120 + 1024*x - 4632*x^2 + 27968*x^3 + 23768*x^4 -2112* x^5 + 184*x^6)/(1-x)^7.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
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MATHEMATICA
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Table[64 n^6 - 480 n^4 + 720 n^2 - 120, {n, 0, 30}] (* or *) CoefficientList[Series[(-120 + 1024 x -4632 x^2 + 27968 x^3 + 23768 x^4 - 2112 x^5 + 184 x^6)/(1-x)^7, {x, 0, 30}], x]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {-120, 184, -824, 14136, 150664, 717880, 2389704}, 30] (* Harvey P. Dale, Apr 08 2019 *)
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PROG
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(Magma) [64*n^6-480*n^4+720*n^2-120: n in [0..30]]; /* or */ I:=[-120, 184, -824, 14136, 150664, 717880, 2389704]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..30]]
(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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