A000950 Number of forests with n nodes and height at most 3.

1, 3, 16, 125, 1176, 12847, 160504, 2261289, 35464816, 612419291, 11539360944, 235469524237, 5170808565976, 121535533284999, 3043254281853496, 80852247370051793, 2270951670959226336, 67221368736302224819, 2091039845329887687136

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..100
• John Riordan, Forests of labeled trees, J. Combin. Theory, 5 (1968), 90-103.

Crossrefs

Cf. A000248, A000949-A000951, A052512-A052514.

Column k=3 of A210725. - Alois P. Heinz, Mar 15 2013

Programs

Mathematica

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 *)

Formula

E.g.f.: exp(x*exp(x*exp(x*exp(x)))).

Extensions

More terms from Vladeta Jovovic, Apr 07 2001