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A304907
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Expansion of x * (d/dx) 1/(1 - Sum_{k>=1} x^k/(1 + x^k)).
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0
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0, 1, 2, 9, 16, 35, 84, 161, 312, 639, 1240, 2354, 4536, 8593, 16128, 30360, 56672, 105213, 195174, 360582, 664040, 1220730, 2238324, 4095035, 7479552, 13636750, 24821108, 45114813, 81887008, 148438211, 268763160, 486082263, 878200416, 1585098372, 2858378368, 5149986275
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OFFSET
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0,3
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COMMENTS
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Sum of all parts of all Carlitz compositions (compositions without adjacent equal parts) of n.
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LINKS
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FORMULA
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MATHEMATICA
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nmax = 35; CoefficientList[Series[x D[1/(1 - Sum[x^k/(1 + x^k), {k, 1, nmax}]), x], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[-(-1)^d, {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[n a[n], {n, 0, 35}]
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CROSSREFS
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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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