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A055356
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Triangle of increasing mobiles (circular rooted trees) with n nodes and k leaves.
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8
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1, 1, 0, 1, 1, 0, 1, 4, 2, 0, 1, 11, 18, 6, 0, 1, 26, 98, 96, 24, 0, 1, 57, 424, 874, 600, 120, 0, 1, 120, 1614, 6040, 8244, 4320, 720, 0, 1, 247, 5682, 35458, 83500, 83628, 35280, 5040, 0, 1, 502, 19022, 187288, 701164, 1169768, 915984, 322560, 40320, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
This is also related to the solution of the equation df/dt=f e^f (see the Maple code). - Frederic Chapoton (fchapoton(AT)voila.fr), Jul 16 2004
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LINKS
| Index entries for sequences related to mobiles
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EXAMPLE
| 1; 1,0; 1,1,0; 1,4,2,0; 1,11,18,6,0; ...
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MAPLE
| P[1]:=1; for n from 1 to 8 do P[n+1]:=simplify((1+n*x)*P[n]+x*diff(P[n], x)) end; (Chapoton)
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CROSSREFS
| Row sums give A029768. Columns 2 through 8: A000295, A055357-A055362.
Sequence in context: A088393 A121225 A049430 * A164789 A028956 A129681
Adjacent sequences: A055353 A055354 A055355 * A055357 A055358 A055359
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KEYWORD
| nonn,tabl
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), May 15 2000
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