A006573 Denominators of an asymptotic expansion for the number of forests on n nodes (A001858). (Formerly M1828)

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

0,4

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.

Links

Table of n, a(n) for n=0..23.

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

Crossrefs

Cf. A006572, A001858, A111999.

Sequence in context: A191999 A101658 A308613 * A009662 A279243 A162218

Adjacent sequences: A006570 A006571 A006572 * A006574 A006575 A006576

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved