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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), 1 <= i <= n, 1 <= j <= n.
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0
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1, 5, 23, 144, 1279, 15035, 219463, 3816512, 76928685, 1762344781, 45207853767, 1283438430208, 39944988007339, 1352308628695895, 49471532968242991, 1944732944768690432, 81748776383970349721, 3659142661552743151353
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OFFSET
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1,2
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COMMENTS
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p divides a(p+1) for odd primes 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=1..n-1} k! = A000178(n-1) (Superfactorials).
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n, j=1..n} i^(j-1).
a(n) = n + Sum_{i=2..n} (i^n-1)/(i-1).
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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