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Search: id:A030238
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| A030238 |
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Backwards shallow diagonal sums of Catalan triangle A009766. |
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+0
6
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| 1, 1, 3, 7, 20, 59, 184, 593, 1964, 6642, 22845, 79667, 281037, 1001092, 3595865, 13009673, 47366251, 173415176, 638044203, 2357941142, 8748646386, 32576869203, 121701491701, 456012458965, 1713339737086
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of linear forests of planted planar trees with n nodes (Christian G. Bower).
Number of ordered trees with n+2 edges and having no branches of length 1 starting from the root. Example: a(1)=1 because the only ordered tree with 3 edges having no branch of length 1 starting from the root is the path tree of length 3. a(n)=A127158(n+2,0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
Hankel transform is A056520. - Paul Barry (pbarry(AT)wit.ie), Oct 16 2007
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FORMULA
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INVERT transform of 1, 2, 2, 5, 14, 42, 132... (cf. A000108).
a(n)=sum{k=0..floor(n/2), (k+1)binomial(2n-3k+1, n-k+1)/(2n-3k+1)}. Diagonal sums of A033184. - Paul Barry (pbarry(AT)wit.ie), Jun 22 2004
a(n)=sum{k=0..floor(n/2), (k+1)binomial(2n-3k, n-k)/(n-k+1)} - Paul Barry (pbarry(AT)wit.ie), Feb 02 2005
G.f.=[1-sqrt(1-4z)]/[z(2-z+z*sqrt(1-4z)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
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MAPLE
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g:=(1-sqrt(1-4*z))/z/(2-z+z*sqrt(1-4*z)): gser:=series(g, z=0, 30): seq(coeff(gser, z, n), n=0..25); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
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MATHEMATICA
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Sum[ triangle[ n-k, (n-k)-(k-1) ], {k, 1, Floor[ (n+1)/2 ]} ]
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CROSSREFS
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Cf. A127158.
Sequence in context: A129429 A084204 A132364 this_sequence A110490 A132868 A056783
Adjacent sequences: A030235 A030236 A030237 this_sequence A030239 A030240 A030241
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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