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A007561 Number of asymmetric rooted connected graphs where every block is a complete graph.
(Formerly M2591)
5
0, 1, 1, 1, 3, 6, 16, 43, 120, 339, 985, 2892, 8606, 25850, 78347, 239161, 734922, 2271085, 7054235, 22010418, 68958139, 216842102, 684164551, 2165240365, 6871792256, 21865189969, 69737972975, 222915760126, 714001019626, 2291298553660, 7366035776888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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]
N. J. A. Sloane, Transforms
FORMULA
Shifts left when weigh-transform applied twice.
a(n) ~ c * d^n / n^(3/2), where d = 3.382016466020272807429818743..., c = 0.161800727760188847021075748... . - Vaclav Kotesovec, Jul 26 2014
MAPLE
g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*g(n-i*j, i-1), j=0..n/i)))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(g(i, i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<1, 0, b(n-1, n-1)):
seq(a(n), n=0..40); # Alois P. Heinz, May 19 2013
MATHEMATICA
g[n_, i_] := g[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := If[n<1, 0, b[n-1, n-1]]; Table[a[n] // FullSimplify, {n, 0, 40}] (* Jean-François Alcover, Feb 11 2014, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A316101.
Sequence in context: A091488 A202839 A371705 * A274295 A192676 A202846
KEYWORD
nonn,nice,eigen
AUTHOR
EXTENSIONS
Additional comments from Christian G. Bower
STATUS
approved

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Last modified April 25 09:38 EDT 2024. Contains 371967 sequences. (Running on oeis4.)