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Search: id:A071725
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| A071725 |
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Expansion of (1+x^2*C^4)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. |
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2
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| 1, 1, 3, 10, 34, 117, 407, 1430, 5070, 18122, 65246, 236436, 861764, 3157325, 11622015, 42961470, 159419670, 593636670, 2217608250, 8308432140, 31212003420, 117544456770, 443690433654, 1678353186780, 6361322162444
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=number of Dyck (n+3)-paths for which the first downstep followed by an upstep (or by nothing at all) is in position 6. For example, a(2)=3 counts UUUUDdUDDD, UUUDDdUUDD, UUUDDdUDUD (the downstep in position 6 is in small type). - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004
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FORMULA
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Contribution from Paul Barry (pbarry(AT)wit.ie), Jun 28 2009: (Start)
E.g.f.: exp(2x)*dif(Bessel_I(1,2x)-Bessel_I(2,2x),x);
a(n)=sum{k=0..n, C(n,k)*2^(n-k)*(-1)^k*C(k+1,floor(k/2))}. (End)
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CROSSREFS
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Essentially the same as A026016.
Sequence in context: A048580 A059738 A094832 this_sequence A026016 A109263 A136439
Adjacent sequences: A071722 A071723 A071724 this_sequence A071726 A071727 A071728
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2002
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