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A307793
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a(1) = 1; a(n+1) = Sum_{d|n} tau(d)*a(d), where tau = number of divisors (A000005).
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2
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1, 1, 3, 7, 24, 49, 205, 411, 1668, 5011, 20095, 40191, 241372, 482745, 1931393, 7725627, 38629803, 77259607, 463562851, 927125703, 5562774334, 22251097753, 89004431205, 178008862411, 1424071142304, 4272213426961, 17088854190591, 68355416767375, 410132502535664, 820265005071329
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x * (1 + Sum_{n>=1} tau(n)*a(n)*x^n/(1 - x^n)).
L.g.f.: -log(Product_{i>=1, j>=1} (1 - x^(i*j))^(a(i*j)/(i*j))) = Sum_{n>=1} a(n+1)*x^n/n.
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MATHEMATICA
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a[n_] := a[n] = Sum[DivisorSigma[0, d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 30}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[DivisorSigma[0, k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 30}]
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PROG
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(PARI) a(n) = if (n==1, 1, sumdiv(n-1, d, numdiv(d)*a(d))); \\ Michel Marcus, Apr 29 2019
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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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