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A364901
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The n-volume of the unit regular n-simplex is sqrt(A364900(n))/a(n), with A364900(n) being squarefree.
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2
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1, 1, 4, 12, 96, 480, 5760, 20160, 215040, 5806080, 116121600, 1277337600, 30656102400, 398529331200, 11158821273600, 83691159552000, 5356234211328000, 30351993864192000, 3278015337332736000, 62282291409321984000, 2491291656372879360000, 52317124783830466560000
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OFFSET
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0,3
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LINKS
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FORMULA
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The n-volume of the unit regular n-simplex is sqrt(n+1)/(n!*2^(n/2)), so a(n) = n! * 2^(n/2) / A000188(n+1) for even n and n! * 2^((n-1)/2) / A000188((n+1)/2) for odd n. It's easy to see that a(n) is an integer.
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EXAMPLE
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n | the n-volume of the
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5 | sqrt(3)/480
6 | sqrt(7)/5760
7 | 1/20160
8 | 1/215040
9 | sqrt(5)/5806080
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PROG
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(PARI) A000188(n) = sqrtint(n/core(n));
a(n) = n! * if(n%2, 2^((n-1)/2)/A000188((n+1)/2), 2^(n/2)/A000188(n+1))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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