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A309509
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G.f. satisfies A(A(x)) = F(x), where F(x) is the g.f. for A001787(n) = n*2^(n-1).
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0
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0, 1, 2, 2, 2, 2, 0, 4, 6, -58, 100, 1052, -5924, -21972, 322020, 332392, -21168682, 29068598, 1724404180, -7070346036, -172304798980, 1290100381724, 20728501384592, -247269172883976, -2936888518668676, 53037176259027580, 477640220538178184
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OFFSET
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0,3
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COMMENTS
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A(x) is sometimes called a functional square root, or half-iterate of F(x).
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LINKS
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MATHEMATICA
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half[q_] := half[q] = Module[{h}, h[0] = 0; h[1] = 1; h[n_Integer] := h[n] = Module[{c}, c[m_Integer /; m < n] := h[m]; c[n] /. Solve[q[n] == Sum[k! c[k] BellY[n, k, Table[m! c[m], {m, n - k + 1}]], {k, n}]/n!, c[n]][[1]]]; h]; a[n_Integer] := a[n] = half[Function[k, k 2^(k-1)]][n]; Table[a[n], {n, 0, 26}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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