A006572 Numerators of an asymptotic expansion for the number of forests on n nodes (A001858).

0, 0, 1, 5, 11, -203, -17207, -3607, 1408301, 8181503, -3299598169, -14983154641, -449428440959, 2480887997789, 19076621521399973, -31806561859970819, -3485566370059659659, -2180443004193000007, 54188073629843061671671

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• 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. A006573, A001858, A111999.

Formula

a(n) = numerator(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