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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
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1, 3, 33, 543, 13857, 504543, 24897057, 1600805343, 130081089057, 13038108350943, 1580312813889057, 227862219988670943, 38547925823643969057, 7561506530728353470943, 1702450746193471070529057
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| a(n) = n!^2 - a(n-1), a(1)=1. - Charles R Greathouse IV, Oct 13 2004
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EXAMPLE
| 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
| a[n_] := Sum[(-1)^j*((n - j)!)^2, {j, 0, n - 1}]
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CROSSREFS
| Cf. A005165, A055546.
Sequence in context: A009502 A011922 A071405 * A083080 A002916 A009659
Adjacent sequences: A092167 A092168 A092169 * A092171 A092172 A092173
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KEYWORD
| easy,nonn
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AUTHOR
| Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 01 2004
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