A000950 Number of forests with n nodes and height at most 3. (Formerly M3025 N1225)

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

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)))).

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 *)

Crossrefs

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

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

Sequence in context: A327826 A157457 A365626 * A320254 A365627 A245012

Adjacent sequences: A000947 A000948 A000949 * A000951 A000952 A000953

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 07 2001

Status

approved