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 A007560 Number of planted identity trees where non-root, non-leaf nodes an even distance from root are of degree 2. (Formerly M0325) 3
 1, 1, 1, 1, 2, 2, 4, 6, 10, 17, 29, 51, 89, 159, 284, 512, 930, 1692, 3101, 5698, 10515, 19464, 36143, 67296, 125622, 235050, 440756, 828142, 1558955, 2939761, 5552744, 10504222, 19899760, 37750091, 71704061, 136361602, 259618770, 494821629, 944074665 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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 = 1..1000 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 2 places left under weigh transform. a(n) ~ c * d^n / n^(3/2), d = 1.983229991815043367273184141..., c = 0.5857451140002020594085469... . - Vaclav Kotesovec, Aug 25 2014 G.f.: x + x^2 * Product_{n>=1} (1 + x^n)^a(n). - Ilya Gutkovskiy, May 09 2019 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))     end: a:= n-> `if`(n<2, n, b(n-2, n-2)): seq(a(n), n=1..50);  # Alois P. Heinz, May 19 2013 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := If[n<2, n, b[n-2, n-2]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 27 2014, after Alois P. Heinz *) CROSSREFS Cf. A007562. Column k=2 of A316074. Sequence in context: A293673 A293505 A032307 * A032237 A276061 A216958 Adjacent sequences:  A007557 A007558 A007559 * A007561 A007562 A007563 KEYWORD nonn,nice,eigen AUTHOR EXTENSIONS Better description from Christian G. Bower, May 15 1998. STATUS approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)