A000951 Number of forests with n nodes and height at most 4. (Formerly M3026 N1226)

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

Offset

1,2

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.

Formula

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

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 *)

Crossrefs

Cf. A000248, A000949, A000950, A052512-A052514.

Column k=4 of A210725. - Alois P. Heinz, Mar 15 2013

Sequence in context: A320254 A365627 A245012 * A000272 A246527 A159594

Adjacent sequences: A000948 A000949 A000950 * A000952 A000953 A000954

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 07 2001

Status

approved