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A308264
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Number of ordered factorizations of n into triangular numbers > 1.
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2
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1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1
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OFFSET
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1,18
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} A(x^(k*(k+1)/2)).
a(1) = 1; a(n) = Sum_{d|n, d<n} A010054(n/d)*a(d).
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MATHEMATICA
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terms = 100; A[_] = 0; Do[A[x_] = x + Sum[A[x^(k (k + 1)/2)], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := If[n == 1, n, Sum[If[(d < n && IntegerQ[Sqrt[8 n/d + 1]]), a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 100}]
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PROG
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(PARI)
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CROSSREFS
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Not the absolute values of A365800.
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KEYWORD
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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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