A000951 Number of forests with n nodes and height at most 4.

1, 3, 16, 125, 1296, 16087, 229384, 3687609, 66025360, 1303751051, 28151798544, 659841763957, 16681231615816, 452357366282655, 13095632549137576, 403040561722348913, 13138626717852194976, 452179922268565180819, 16381932383826669204640

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, A000950, A052512-A052514.

Column k=4 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*Exp[x]]]]], {x, 0, nn}], x] (* T. D. Noe, Jun 21 2012 *)

Formula

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

Extensions

More terms from Vladeta Jovovic, Apr 07 2001