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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 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.)