A006572 Numerators of an asymptotic expansion for the number of forests on n nodes (A001858). (Formerly M3817)

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

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..18.

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

Crossrefs

Cf. A006573, A001858, A111999.

Sequence in context: A229907 A181491 A375161 * A184934 A159009 A230841

Adjacent sequences: A006569 A006570 A006571 * A006573 A006574 A006575

Keyword

sign,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