

A241555


Triangle read by rows: Number T(n,k) of 2colored 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
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OFFSET

0,5


COMMENTS

T(n,k) = T(n,nk) 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 (* JeanFrançois Alcover, Sep 24 2019, from PARI *)


PROG

(PARI)
B(n)={my(u=vector(n)); u[1]=1; for(n=1, #u1, u[n+1]=(1+y)*(sum(i=1, n, u[i]*u[n+1i]) + 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



