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Search: id:A092170
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| A092170 |
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Sum of squares of alternating factorials : n!^2 - (n-1)!^2 + (n-2)!^2 - ... 1!^2. |
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+0
1
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| 1, 3, 33, 543, 13857, 504543, 24897057, 1600805343, 130081089057, 13038108350943, 1580312813889057, 227862219988670943, 38547925823643969057, 7561506530728353470943, 1702450746193471070529057
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The height of a regular simplex (hypertetrahedron) of dimension n and with unit length edges will be h(n)=sqrt(a(n))/n!. The contents (hypervolume) will then be V(n)=V(n-1)*h(n)/n where V(1)=1.
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FORMULA
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a(n) = n!^2 - a(n), a(1)=1.
a(n) = n!^2 - a(n-1), a(1)=1. - Charles R. Greathouse (greathcr(AT)muohio.edu), Oct 13 2004
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EXAMPLE
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a(3)=3!^2-a(2)=36-a(2);
a(2)=2!^2-a(1)=4-a(1)=3-1=3 ->
a(3)=36-3=33.
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MATHEMATICA
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a[n_] := Sum[(-1)^j*((n - j)!)^2, {j, 0, n - 1}]
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CROSSREFS
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Cf. A005165, A055546.
Sequence in context: A009502 A011922 A071405 this_sequence A083080 A002916 A009659
Adjacent sequences: A092167 A092168 A092169 this_sequence A092171 A092172 A092173
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KEYWORD
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easy,nonn
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AUTHOR
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Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 01 2004
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