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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-François Alcover, Feb 11 2014, after Alois P. Heinz *) CROSSREFS Cf. A007563, A035079-A035081. Column k=2 of A316101. Sequence in context: A091488 A202839 A371705 * 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 April 25 09:38 EDT 2024. Contains 371967 sequences. (Running on oeis4.)