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A005199 a(n) = Sum_t t*F(n,t), where F(n,t) is the number of forests with n (unlabeled) nodes and exactly t trees, all of which are planted (that is, rooted trees in which the root has degree 1).
(Formerly M3285)
0
0, 1, 1, 4, 6, 18, 35, 93, 214, 549, 1362, 3534, 9102, 23951, 63192, 168561, 451764, 1219290, 3305783, 9008027, 24643538, 67681372, 186504925, 515566016, 1429246490 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The triangular array F(n,t) (analogous to A095133 for A005196 and A033185 for A005197) seems not to be in the OEIS yet.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..25.

E. M. Palmer and A. J. Schwenk, On the number of trees in a random forest, J. Combin. Theory, B 27 (1979), 109-121.

CROSSREFS

Sequence in context: A281861 A218898 A088810 * A107390 A051253 A175955

Adjacent sequences:  A005196 A005197 A005198 * A005200 A005201 A005202

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Definition clarified by N. J. A. Sloane, May 29 2012

STATUS

approved

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Last modified October 15 11:25 EDT 2018. Contains 316224 sequences. (Running on oeis4.)