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A293840
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E.g.f.: exp(Sum_{n>=1} A000009(n)*x^n).
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11
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1, 1, 3, 19, 121, 1041, 10651, 121843, 1575729, 22970881, 366805171, 6365365491, 120044573353, 2430782532049, 52677233993931, 1217023986185491, 29799465317716321, 771272544315151233, 21044341084622337379, 603173026772647474771
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OFFSET
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0,3
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COMMENTS
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The congruence a(n+k) == a(n) (mod k) holds for all n and k.
It follows that the sequence obtained by taking a(n) modulo a fixed positive integer k is periodic with exact period dividing k. For example, the sequence taken modulo 10 becomes [1, 1, 3, 9, 1, 1, 1, 3, 9, 1, ...], a purely periodic sequence with exact period 5.
3 divides a(3*n+2); 9 divides a(9*n+8); 11 divides a(11*n+4); 19 divides a(19*n+3). (End)
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LINKS
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FORMULA
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a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A000009(k)*a(n-k)/(n-k)! for n > 0.
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MATHEMATICA
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nmax = 20; CoefficientList[Series[E^Sum[PartitionsQ[k]*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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