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A000949
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Number of forests with n nodes and height at most 2.
(Formerly M3021 N1223)
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11
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1, 1, 3, 16, 101, 756, 6607, 65794, 733833, 9046648, 121961051, 1782690174, 28055070397, 472594822324, 8479144213191, 161340195463066, 3243707386310033, 68679247688467056, 1526976223741111987, 35557878951515668726, 865217354118762606021, 21952682834849990904556
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| J. Riordan, Forests of labeled trees, J. Combin. Theory, 5 (1968), 90-103.
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).
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FORMULA
| E.g.f.: exp(x*exp(x*exp(x))).
a(n)=n!*sum(m=1..n-1, sum(k=1..n-m, (k^(n-m-k)*m^k)/(k!*(n-m-k)!))/m!)+1; [From Vladimir Kruchinin, May 28 2011]
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PROG
| (Maxima)
a(n):=n!*sum(sum((k^(n-m-k)*m^k)/(k!*(n-m-k)!), k, 1, n-m)/m!, m, 1, n-1)+1; [From Vladimir Kruchinin, May 28 2011]
(Pari) x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x*exp(x*exp(x))))) /* show terms, with a(0)=1 */ /* Joerg Arndt, May 28 2011 */
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CROSSREFS
| Cf. A000248, A000950, A000951, A052512-A052514.
Sequence in context: A137572 A009151 A009007 * A091637 A074542 A105622
Adjacent sequences: A000946 A000947 A000948 * A000950 A000951 A000952
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2001
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