A091315 Number of orbits of length n under the map whose periodic points are counted by A061684.

1, 2, 21, 402, 13805, 761154, 62523664, 7237970648, 1132600004910, 231900134422880, 60528794385067778, 19713593779259862624, 7869483395065035685162, 3792402572391137423764584

Offset

1,2

Comments

Old name was: A061684 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n.

Links

Table of n, a(n) for n=1..14.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Thomas Ward, Exactly realizable sequences. [local copy].

Formula

If b(n) is the (n+1)th term in A061684, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).

Example

The sequence A061684 begins 1,1,5,64,1613, so a(3)=(b(3)-b(1))/3=21.

Crossrefs

Cf. A061684.

Sequence in context: A216281 A263625 A245686 * A359716 A087546 A090729

Adjacent sequences: A091312 A091313 A091314 * A091316 A091317 A091318

Keyword

nonn

Author

Thomas Ward, Feb 24 2004

Extensions

Name clarified by Michel Marcus, May 14 2015

Status

approved