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A051846
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Digits 1..n in strict descending order n..1 interpreted in base n+1.
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11
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1, 7, 57, 586, 7465, 114381, 2054353, 42374116, 987654321, 25678050355, 736867805641, 23136292864686, 789018236134297, 29043982525261081, 1147797409030816545, 48471109094902544776, 2178347851919531492065, 103805969587115219182431
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OFFSET
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1,2
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COMMENTS
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All odd-indexed (2n+1) terms are divisible by (2n+1). See A051847.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} i*(n+1)^(i-1).
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EXAMPLE
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a(1) = 1,
a(2) = 2*3 + 1 = 7,
a(3) = 3*(4^2) + 2*4 + 1 = 57,
a(4) = 4*(5^3) + 3*(5^2) + 2*5 + 1 = 586.
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MAPLE
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a(n) := proc(n) local i; add(i*((n+1)^(i-1)), i=1..n); end;
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MATHEMATICA
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PROG
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(PARI) a(n)=((n+1)^(n+1)*(n-1)+1)/n^2
(Maxima) makelist(((n+1)^(n+1)*(n-1) + 1)/n^2, n, 1, 20); /* Martin Ettl, Jan 25 2013 */
(Python)
def a(n): return sum((i+1)*(n+1)**i for i in range(n))
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CROSSREFS
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KEYWORD
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easy,base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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