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A094149 The 2k-th moments of the random graph G(n, 1/n) (odd moments are zero). The number of walks of length 2k on _all_ bushes (rooted plane trees) that start and end at the root and visit new vertices from left-to-right (but may return). 0
1, 3, 12, 57, 303, 1747, 10727, 69331, 467963, 3280353, 23785699, 177877932, 1368977132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

A. Spiridonov, Spectra of sparse graphs and matrices, in preparation, contact submitter for preprints.

LINKS

Table of n, a(n) for n=1..13.

A. Khorunzhy, On asymptotic solvability of random graph's laplacians, preprint, 2000

FORMULA

See [link:1] for a complex recurrence relationship. Asymptotically between A_k (the k-th Bell number, A000110) and choose(2k, k)*A_k. (see [ref:1]).

EXAMPLE

The bushes with 1..3 edges (counted by the Catalan numbers, A000108):

*...*...*...*....*....*....*...*

|../.\..|../|\../.\../.\...|...|

........|.......|......|../.\..|

...............................|

1 + 0 + 0 + 0 +. 0 +. 0 +. 0 + 0 + ... = 1 = number of walks of length 1

1 + 1 + 1 + 0 +. 0 +. 0 +. 0 + 0 + ... = 3 = number of walks of length 2

1 + 3 + 3 + 1 +. 1 +. 1 +. 1 + 1 + ... = 12 = number of walks of length 3

CROSSREFS

Cf. A000108, A000110.

Sequence in context: A243521 A151498 A103370 * A291695 A117107 A159609

Adjacent sequences:  A094146 A094147 A094148 * A094150 A094151 A094152

KEYWORD

nonn

AUTHOR

Alexey Spiridonov (aspirido(AT)princeton.edu), May 04 2004

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)