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A051573
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INVERTi transform of A000081 = [1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12486,...].
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6
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1, 1, 1, 2, 3, 8, 16, 41, 98, 250, 631, 1646, 4285, 11338, 30135, 80791, 217673, 590010, 1606188, 4392219, 12055393, 33206321, 91752211, 254261363, 706465999, 1967743066, 5493195530, 15367129299, 43073007846, 120949992543, 340206026166, 958444631917
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148175241..., c = A187770 = 0.4399240125710253040409033914... . - Vaclav Kotesovec, Sep 06 2014
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MAPLE
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with(numtheory):
b:= proc(n) option remember; local d, j; `if` (n<2, n,
(add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
end:
a:= proc(n) option remember; local i; `if`(n<0, -1,
-add(a(n-i) *b(i+1), i=1..n+1))
end:
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MATHEMATICA
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b[n_] := b[n] = If[n < 2, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; a[n_] := a[n] = If[n < 0, -1, -Sum[a[n-i]*b[i+1], {i, 1, n+1}]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 16 2014, after Alois P. Heinz *)
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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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