A006573 Denominators of an asymptotic expansion for the number of forests on n nodes (A001858).

1, 1, 1, 2, 8, 16, 384, 768, 3072, 6144, 1474560, 589824, 11796480, 7864320, 11890851840, 23781703680, 95126814720, 27179089920, 91321742131200, 7305739370496, 730573937049600, 1461147874099200, 385743038762188800, 771486077524377600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Comments

Takacs Table 2 gives incorrect A006572(10)/A006573(10) = -137483257/61440 and A006572(11)/A006573(11) = -24971924401/983040. - Sean A. Irvine, May 11 2017

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• L. Takacs, On the number of distinct forests, SIAM J. Discrete Math., 3 (1990), 574-581.

Crossrefs

Cf. A006572, A001858, A111999.

Formula

a(n) = denom(Sum_{i=1..floor(n/2)} (-1)^(i-1) * |A111999(n, 2*i-1)| / (2^(n-i) * (n-i)!)). - Sean A. Irvine, May 11 2017

Extensions

a(10) and a(11) corrected and more terms from Sean A. Irvine, May 11 2017