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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
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
Sequence in context: A137327 A143913 A228815 * A277741 A241138 A241349
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 February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)