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%I M3025 N1225 #21 May 19 2024 14:03:19
%S 1,3,16,125,1176,12847,160504,2261289,35464816,612419291,11539360944,
%T 235469524237,5170808565976,121535533284999,3043254281853496,
%U 80852247370051793,2270951670959226336,67221368736302224819,2091039845329887687136
%N Number of forests with n nodes and height at most 3.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000950/b000950.txt">Table of n, a(n) for n = 1..100</a>
%H John Riordan, <a href="https://doi.org/10.1016/S0021-9800(68)80033-X">Forests of labeled trees</a>, J. Combin. Theory, 5 (1968), 90-103.
%F E.g.f.: exp(x*exp(x*exp(x*exp(x)))).
%t nn = 20; Range[0, nn]! CoefficientList[Series[Exp[x*Exp[x*Exp[x*Exp[x]]]], {x, 0, nn}], x] (* _T. D. Noe_, Jun 21 2012 *)
%Y Cf. A000248, A000949-A000951, A052512-A052514.
%Y Column k=3 of A210725. - _Alois P. Heinz_, Mar 15 2013
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Apr 07 2001