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 A007549 Number of increasing rooted connected graphs where every block is a complete graph. (Formerly M2977) 8
 1, 1, 3, 14, 89, 716, 6967, 79524, 1041541, 15393100, 253377811, 4596600004, 91112351537, 1959073928124, 45414287553455, 1129046241331316, 29965290866974493, 845605519848379436, 25282324544244718411, 798348403914242674980, 26549922456617388029641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS In an increasing rooted graph, nodes are numbered and the numbers increase as you move away from the root. (a(n+1)/a(n))/n tends to 1/A073003 = 1.676875... (same limit as A029768). - Vaclav Kotesovec, Jul 26 2014 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi and Vaclav Kotesovec, Table of n, a(n) for n = 1..410 (first 200 terms from Vincenzo Librandi) M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] FORMULA Shifts left when exponentiated twice. MAPLE exptr:= proc(p) local g; g:= proc(n) option remember; p(n) +add(binomial(n-1, k-1) *p(k) *g(n-k), k=1..n-1) end: end: b:= exptr(exptr(a)): a:= n-> `if`(n=0, 1, b(n-1)): seq(a(n), n=1..30); # Alois P. Heinz, Oct 07 2008 MATHEMATICA exptr[p_] := Module[{g}, g[n_] := g[n] = p[n] + Sum[ Binomial[n-1, k-1]*p[k]*g[n-k], {k, 1, n-1}]; g]; b = exptr[ exptr[a] ]; a[n_] := If[n == 0, 1, b[n-1]]; Table[ a[n], {n, 1, 19}] (* Jean-François Alcover, May 10 2012, after Alois P. Heinz *) CROSSREFS Cf. A007563, A030019, A035051-A035053. Cf. A029768. Sequence in context: A199548 A038170 A007840 * A081005 A074518 A200317 Adjacent sequences:  A007546 A007547 A007548 * A007550 A007551 A007552 KEYWORD nonn,eigen,nice AUTHOR EXTENSIONS New description from Christian G. Bower, Oct 15 1998 STATUS approved

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Last modified February 22 05:52 EST 2020. Contains 332116 sequences. (Running on oeis4.)