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Search: id:A118714
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| A118714 |
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Determinant of n X n matrix whose diagonal are the first n tetrahedral numbers and all other elements are 1's. |
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+0
1
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| 1, 3, 27, 513, 17442, 959310, 79622730, 9475104870, 1553917198680, 340307866510920, 96987741955612200, 35206550329887228600, 15983773849768801784400, 8934929582020760197479600
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OFFSET
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1,2
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COMMENT
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a(n+2) / a(n+1) = A062748(n) = A062745(n+2, 3)= binomial(n+4, 3)-1 = (n+1)*(n^2+8*n+18)/3!.
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FORMULA
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a(n) = Det[ DiagonalMatrix[ Table[ i*(i+1)(i+2)/6 - 1, {i, 1, n} ] ] + 1 ]. a(n) = Product[(j-3)*(j^2+2)/3!,{j,4,n+2}]. a(n) = Product[(k+1)*(k^2+8*k+18)/3!,{k,0,n-2}] = Product[A062748(k),{k,0,n-2}].
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EXAMPLE
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The matrix begins:
1 1 1 1 1 1 1 ...
1 4 1 1 1 1 1 ...
1 1 10 1 1 1 1 ...
1 1 1 20 1 1 1 ...
1 1 1 1 35 1 1 ...
1 1 1 1 1 56 1 ...
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MATHEMATICA
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Table[ Det[ DiagonalMatrix[ Table[ i*(i+1)(i+2)/6 - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]. Table[Product[(k-3)*(k^2+2)/3!, {k, 4, n+2}], {n, 1, 20}]
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CROSSREFS
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Cf. A000292, A067550, A062748, A062745.
Sequence in context: A159600 A159601 A111844 this_sequence A089506 A062496 A099084
Adjacent sequences: A118711 A118712 A118713 this_sequence A118715 A118716 A118717
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 20 2006
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