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A011274
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Triangle of numbers of hybrid rooted trees (divided by Fibonacci numbers).
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1
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1, 2, 1, 7, 4, 1, 31, 18, 6, 1, 154, 90, 33, 8, 1, 820, 481, 185, 52, 10, 1, 4575, 2690, 1065, 324, 75, 12, 1, 26398, 15547, 6276, 2006, 515, 102, 14, 1, 156233, 92124, 37711, 12468, 3420, 766, 133, 16, 1, 943174, 556664, 230277, 78030, 22412, 5439, 1085, 168, 18, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Triangle T(n,k) = [x^(n-k)] A(x)^k where A(x) is the o.g.f. of A007863. - Vladimir Kruchinin, Mar 17 2011
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LINKS
| Vladimir Kruchinin, Compositae and their properties, arXiv:1103.2582
J. M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50 (1994) 135-145.
Index entries for sequences related to rooted trees
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FORMULA
| T(n,k) = k/n *sum_{i=0..n-k} binomial(i+n-1,n-1)*binomial(i+n,n-k-i). - Vladimir Kruchinin Mar 17 2011
r/(m*n+r) *T((m+1)*n+r,m*n+r) =sum_{k=1..n} k*T((m+1)*n-k,m*n) *T(r+k,r)/n. - Vladimir Kruchinin, Mar 17 2011
T(n,m)= (m/n) *sum_{k=1..n-m+1} k *A007863(k-1) *T(n-k,m-1), 1<m<=n. - Vladimir Kruchinin, Mar 17 2011
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EXAMPLE
| 1;
2,1;
7,4,1;
31,18,6,1;
154,90,33,8,1;
820,481,185,52,10,1;
4575,2690,1065,324,75,12,1;
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MAPLE
| A011274 := proc(n, k) k/n*add( binomial(i+n-1, n-1)*binomial(i+n, n-k-i), i=0..n-k) ; end proc: # R. J. Mathar, Mar 21 2011
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MATHEMATICA
| t[n_, k_] := k/n*Binomial[n, k]*HypergeometricPFQ[ {k-n, n, n+1}, {1/2 + k/2, 1+k/2}, -1/4]; Flatten[ Table[ t[n, k], {n, 1, 10}, {k, 1, n}]] (* From Jean-François Alcover, Dec 02 2011, after Vladimir Kruchinin *)
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PROG
| (Maxima)
A011274(n, k):=k/n*sum(binomial(i+n-1, n-1)*binomial(i+n, n-k-i), i, 0, n-k); /* Vladimir Kruchinin, Mar 17 2011 */
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CROSSREFS
| Cf. A011270, A011272.
Sequence in context: A072248 A177011 A092276 * A122843 A167196 A107865
Adjacent sequences: A011271 A011272 A011273 * A011275 A011276 A011277
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KEYWORD
| nonn,easy,tabl,nice
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AUTHOR
| pallo(AT)u-bourgogne.fr (Jean Pallo)
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