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A054516
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Equivalent of the Kurepa hypothesis for left factorial.
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2
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0, 2, 2, 6, -4, 50, -258, 1862, -14824, 133506, -1334950, 14684582, -176214828, 2290792946, -32071101034, 481066515750, -7697064251728, 130850092279682, -2355301661033934, 44750731559645126, -895014631192902100, 18795307255050944562, -413496759611120779858
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OFFSET
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3,2
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LINKS
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FORMULA
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a(3) = 0, a(n) = -(n-3)*a(n-1) + (n-3)*(n-2).
Conjecture: (-n+4)*a(n) + (-n^2+8*n-14)*a(n-1) + (n-2)*(n-4)*a(n-2) = 0. - R. J. Mathar, Jan 31 2014
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MATHEMATICA
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(* Assuming offset 0 *)
Table[(-1)^n*n*((-1)^n - Subfactorial[n - 1]), {n, 0, 20}] (* Peter Luschny, Dec 30 2016 *)
RecurrenceTable[{a[n]+(n-3)*a[n-1]==(n-2)*(n-3), a[3]==0}, a, {n, 3, 30}] (* G. C. Greubel, Mar 30 2019 *)
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PROG
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(PARI) m=30; v=concat([0], vector(m-1)); for(n=2, m, v[n]=-(n-1)*v[n-1] + n*(n-1)); v \\ G. C. Greubel, Mar 30 2019
(Magma) [n eq 3 select 0 else -(n-3)*Self(n-3) + (n-2)*(n-3): n in [3..30]]; // G. C. Greubel, Mar 30 2019
(Sage)
@CachedFunction
def Self(n):
if n == 3 : return 0
return -(n-3)*Self(n-1) + (n-2)*(n-3)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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