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A030017
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a(1) = 1, a(n+1) = Sum_{k = 1..n} p(k)*a(n+1-k), where p(k) is the k-th prime.
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16
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1, 2, 7, 25, 88, 311, 1095, 3858, 13591, 47881, 168688, 594289, 2093693, 7376120, 25986209, 91549913, 322532092, 1136286727, 4003159847, 14103208628, 49685873471, 175044281583, 616684348614, 2172590743211, 7654078700221, 26965465508072, 94999850216565
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OFFSET
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1,2
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COMMENTS
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Apply "INVERT" transform to primes.
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LINKS
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FORMULA
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INVERT: a's from b's in 1+Sum a_i x^i = 1/(1-Sum b_i x^i).
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EXAMPLE
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a(5) = 25*2 +7*3 +2*5 + 1*7 = 88.
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MAPLE
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a:= proc(n) option remember; `if`(n=1, 1,
add(a(n-i)*ithprime(i), i=1..n-1))
end:
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MATHEMATICA
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CoefficientList[ Series[ 1/(1 - Sum[ Prime[ n ]*x^n, {n, 1, 25} ] ), {x, 0, 25} ], x ]
(* Second program: *)
a[1] = 1; a[m_] := a[m] = Sum[Prime@ k a[m - k], {k, m - 1}]; Table[a@ n, {n, 25}] (* Michael De Vlieger, Dec 13 2016 *)
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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STATUS
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approved
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