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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

Alois P. Heinz, Table of n, a(n) for n = 0..1900

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-Fran├žois Alcover, Feb 11 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A007563, A035079-A035081.

Column k=2 of A316101.

Sequence in context: A019497 A091488 A202839 * A274295 A192676 A202846

Adjacent sequences:  A007558 A007559 A007560 * A007562 A007563 A007564

KEYWORD

nonn,nice,eigen

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional comments from Christian G. Bower

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)