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A319590 Number of binary rooted trees with n leaves spanning an initial interval of positive integers and all non-leaf nodes having out-degree 2. 2
1, 2, 8, 58, 576, 7440, 117628, 2201014, 47552012, 1164812674, 31898271660, 965666303078, 32022547868872, 1154362247246714, 44945574393963472, 1879720975031634318, 84039891496643620196, 3999886612000379135606, 201919706444252727224852, 10775953237291840618917900 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

MAPLE

b:= proc(n, k) option remember; `if`(n<2, k*n, `if`(n::odd, 0,

      (t-> t*(1-t)/2)(b(n/2, k)))+add(b(i, k)*b(n-i, k), i=1..n/2))

    end:

a:= n-> add(add((-1)^i*binomial(k, i)*b(n, k-i), i=0..k), k=0..n):

seq(a(n), n=1..23);  # Alois P. Heinz, Sep 07 2019

PROG

(PARI) \\ here R(n, k) is k-th column of A319539 as a vector.

R(n, k)={my(v=vector(n)); v[1]=k; for(n=2, n, v[n]=sum(j=1, (n-1)\2, v[j]*v[n-j]) + if(n%2, 0, binomial(v[n/2]+1, 2))); v}

seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )}

CROSSREFS

Row sums of A319541.

Cf. A316651, A319539.

Sequence in context: A308352 A185898 A063074 * A005804 A162067 A179534

Adjacent sequences:  A319587 A319588 A319589 * A319591 A319592 A319593

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Sep 23 2018

STATUS

approved

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Last modified November 20 13:03 EST 2019. Contains 329336 sequences. (Running on oeis4.)