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Search: id:A128884
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| A128884 |
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Sum of all matrix elements of n X n Vandermonde matrix of numbers 1,2,..n, i.e. the matrix A with A[i,j] = i^j, 1 <= i <= n, 0 <= j <= n-1. |
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1
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| 1, 5, 23, 144, 1279, 15035, 219463, 3816512, 76928685, 1762344781, 45207853767, 1283438430208, 39944988007339, 1352308628695895, 49471532968242991, 1944732944768690432, 81748776383970349721, 3659142661552743151353
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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p divides a(p+1) for an odd prime p. p^2 divides a(p+1) for prime p = {3, 7, 71, ...}. Determinant of n X n Vandermonde matrix of numbers 1,2,..n equals Product[ k!, {k,1,n-1} ] = A000178(n-1) Superfactorials.
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics, Vandermonde Matrix.
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FORMULA
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a(n) = Sum[ i^j, {i,1,n}, {j,0,n-1} ]. a(n) = n + Sum[(i^n-1)/(i-1), {i,2,n} ].
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MATHEMATICA
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Table[ n + Sum[ (i^n-1)/(i-1), {i, 2, n} ], {n, 1, 25} ]
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CROSSREFS
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Cf. A060946 = Trace of Vandermonde matrix of numbers 1, 2, ..n. Cf. A000178 = Superfactorials: product of first n factorials.
Sequence in context: A129098 A047049 A020034 this_sequence A007836 A054749 A107204
Adjacent sequences: A128881 A128882 A128883 this_sequence A128885 A128886 A128887
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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), Apr 18 2007
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