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A048285
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Number of Dyck paths of length 2n with nondecreasing peaks.
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2
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1, 2, 4, 9, 21, 51, 126, 316, 800, 2040, 5230, 13464, 34773, 90035, 233590, 607011, 1579438, 4114014, 10725109, 27979704, 73035818, 190737623, 498320800, 1302341411, 3404552915, 8902154847, 23281653957, 60897957049, 159312797657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The name refers to weakly increasing peaks. The case of strictly increasing peaks is counted by A008930. - David Callan (callan(AT)stat.wisc.edu), Feb 18 2004
a(n) ~ 0.11997*[(3+sqrt(5))/2]^n (Theorem 2 of the Penaud-Roques paper). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2008
Row sums of A138155. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2008
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REFERENCES
| J. G. Penaud and O. Roques, Generation de chemins de Dyck a pics croissants, Discrete Mathematics, Vol. 246, no. 1-3 (2002), 255-267.
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FORMULA
| G.f.: sum_{n >= 0} {(-1)^n x^{2n+1}(1-x)}/ {prod_{i=1...n+1}((1-x)(1-x^i)-x)}
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EXAMPLE
| a(3)=4 because we have UDUDUD, UDUUDD, UUDUDD and UUUDDD, where U=(1,1) and D=(1,-1).
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MAPLE
| g:=sum((-1)^n*z^(2*n+1)*(1-z)/(product((1-z)*(1-z^i)-z, i=1..n+1)), n=0..40): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=1..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2008
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CROSSREFS
| Cf. A138155.
Sequence in context: A199410 A091600 A176334 * A051529 A005207 A094286
Adjacent sequences: A048282 A048283 A048284 * A048286 A048287 A048288
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KEYWORD
| nonn
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AUTHOR
| Olivier Roques (roques(AT)labri.u-bordeaux.fr)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2008
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