growth of A000081

[David Broadhurst]

Let a(n) be the number of rooted trees with n nodes, as in EIS A000081.
Let c=\lim_{n\to\infty} a(n+1)/a(n). Then to 920 digits, I find that c=

2.955765285651994974714817524123194588375492304663596595350472478905964733139574
95108666828367658135253066437135530622161408047163980868055281302523447959106564
50830094857724237733381960025839469497653106826655718270860682985427979012044927
31826487792316554344188604980905338695147812632425169980984247645411702291449818
22077313053266914888228708798846742250790069720415592628267243466038655113955499
74595716724047293015669814373335868696232253972389009814080091539603396562978537
73424688143338850359837659876253352922914796047050868038844907201785223166133081
21592931009017474487054085445999453144877589534799482040374971599124794405012732
50666044628064269870751284766131175952434919430350883603512578989841518484797085
22341295301401844049627168030505046359254051318103363418265067206604638096279928
67589182570876694613490693392683201388939972660741789592475866252053043776954947
26802194622430816490355172525009444586418

Can this constant be related to others? So far, I failed to identify it.

David Broadhurst