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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-Fran├žois 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

N. J. A. Sloane

EXTENSIONS

New description from Christian G. Bower, Oct 15 1998

STATUS

approved

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Last modified February 25 20:40 EST 2018. Contains 299656 sequences. (Running on oeis4.)