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 A000106 2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees. (Formerly M1415 N0553) 13
 1, 2, 5, 12, 30, 74, 188, 478, 1235, 3214, 8450, 22370, 59676, 160140, 432237, 1172436, 3194870, 8741442, 24007045, 66154654, 182864692, 506909562, 1408854940, 3925075510, 10959698606, 30665337738, 85967279447, 241433975446, 679192039401, 1913681367936, 5399924120339 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 2..1000 (terms n = 2..200 from T. D. Noe) Vsevolod Gubarev, Rota-Baxter operators on a sum of fields, arXiv:1811.08219 [math.RA], 2018. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 385 FORMULA Self-convolution of rooted trees A000081. a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.87984802514205060808180678... . - Vaclav Kotesovec, Sep 11 2014 In the asymptotics above the constant c = 2 * A187770. - Vladimir Reshetnikov, Aug 13 2016 MAPLE b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-1)^2, x=0, n+1), x, n): seq(a(n), n=2..35); # Alois P. Heinz, Aug 21 2008 MATHEMATICA <

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Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)