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 A241555 Triangle read by rows: Number T(n,k) of 2-colored binary rooted trees with n nodes and exactly k <= n nodes of a specific color. 4
 1, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 11, 16, 11, 3, 6, 26, 50, 50, 26, 6, 11, 60, 143, 188, 143, 60, 11, 23, 142, 404, 656, 656, 404, 142, 23, 46, 334, 1105, 2143, 2652, 2143, 1105, 334, 46, 98, 794, 2995, 6737, 9934, 9934, 6737, 2995, 794, 98, 207, 1888, 7999, 20504, 35080, 41788, 35080, 20504, 7999, 1888, 207 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k) = T(n,n-k) by definition. First column is A001190. Row sums are given by A226909. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1274 EXAMPLE Triangle begins:    1;    1,   1;    1,   2,   1;    2,   5,   5,   2;    3,  11,  16,  11,  3;    6,  26,  50,  50,  26,   6;   11,  60, 143, 188, 143,  60,  11;   23, 142, 404, 656, 656, 404, 142, 23;   ... MATHEMATICA B[m_] := Module[{u}, u = Table[0, {m}]; u[[1]] = 1; For[n = 1, n <= Length[u] - 1, n++, u[[n + 1]] = (1 + y)*(Sum[u[[i]]*u[[n + 1 - i]], {i, 1, n}] + If[OddQ[n], u[[Quotient[n, 2] + 1]] /. y -> y^2, 0])/2]; u]; CoefficientList[#, y]& /@ B[11] // Flatten (* Jean-François Alcover, Sep 24 2019, from PARI *) PROG (PARI) B(n)={my(u=vector(n)); u[1]=1; for(n=1, #u-1, u[n+1]=(1+y)*(sum(i=1, n, u[i]*u[n+1-i]) + if(n%2, subst(u[n\2+1], y, y^2)))/2); u} { my(A=B(10)); for(n=1, #A, print(Vec(A[n]))) } \\ Andrew Howroyd, May 21 2018 CROSSREFS Cf. A001190, A226909. Sequence in context: A137327 A143913 A228815 * A277741 A241138 A241349 Adjacent sequences:  A241552 A241553 A241554 * A241556 A241557 A241558 KEYWORD nonn,tabl AUTHOR David Serena, May 17 2014 EXTENSIONS Edited by Nathaniel Johnston, Sep 11 2014 Missing term inserted and a(45) and beyond from Andrew Howroyd, May 21 2018 STATUS approved

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Last modified September 23 16:38 EDT 2020. Contains 337314 sequences. (Running on oeis4.)