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%I #19 Nov 07 2015 03:24:12
%S 1,-1,1,1,-14,64,-97,-1376,15915,-68820,-467868,11504693,-85105325,
%T -490922106,21504158897,-242026388646,-848338391966,80509815160192,
%U -1351044945506956,1506218518200935,472249651021870475,-11783220545826576339,78093421491085905492
%N Exponential reversion of rooted trees A000081.
%H Alois P. Heinz, <a href="/A050396/b050396.txt">Table of n, a(n) for n = 1..100</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%t a[n:0|1] := n; a[n_] := a[n] = Sum[m a[m] a[n-k*m], {m, n-1}, {k, (n-1)/m}]/(n-1); length = 20; Range[length]! InverseSeries[Sum[a[n] x^n/n!, {n, 0, length}] + O[x]^(length+1)][[3]] (* _Vladimir Reshetnikov_, Nov 06 2015 *)
%Y Cf. A050395.
%K sign
%O 1,5
%A _Christian G. Bower_, Nov 15 1999
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