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A005195
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Number of forests with n unlabeled nodes.
(Formerly M0776)
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14
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1, 1, 2, 3, 6, 10, 20, 37, 76, 153, 329, 710, 1601, 3658, 8599, 20514, 49905, 122963, 307199, 775529, 1977878, 5086638, 13184156, 34402932, 90328674, 238474986, 632775648, 1686705630, 4514955632, 12132227370, 32717113805, 88519867048
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, pp. 58-59.
E. M. Palmer and A. J. Schwenk, On the number of trees in a random forest, J. Combin. Theory, B 27 (1979), 109-121.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| Euler transform of A000055: Product_{n>0} (1-x^n)^(-A000055(n)). a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), where b(k) = Sum_{d divides k} d*A000055(d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 05 2002
G.f.: exp(sum_{k>0} B(x^k)/k ), where B(x) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 6*x^6 + 11*x^7 + ... = (C(x)-1)/x and C is the g.f. for A000055.
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CROSSREFS
| Cf. A000055. Row sums of A136605. A diagonal of A144215.
Sequence in context: A093371 A003214 A123423 * A052843 A120707 A047111
Adjacent sequences: A005192 A005193 A005194 * A005196 A005197 A005198
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KEYWORD
| nonn,easy,nice
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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), Sep 05 2002
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