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Search: id:A035929
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| A035929 |
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Number of Dyck paths starting U^mD^m (an m-pyramid), followed by a pyramid-free Dyck path. |
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+0
2
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| 0, 1, 1, 1, 2, 6, 19, 61, 200, 670, 2286, 7918, 27770, 98424, 351983, 1268541, 4602752, 16799894, 61642078, 227239086, 841230292, 3126039364, 11656497518, 43601626146, 163561902392, 615183356156
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Hankel transform is -A128834. [From Paul Barry (pbarry(AT)wit.ie), Jul 04 2009]
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FORMULA
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G.f.: (2x)/(1+x + sqrt(1-4x)).
G.f. satisfies A^2*(x^2-2*x+2)-A*(x+1)+x = 0.
The generating function can be written as x/(1-x) times that of A082989.
G.f.: (2x)/(1+x+(1-x)*sqrt(1-4x)); 1/(1-x(1-x)/(1-x/(1-x/(1-x/(1-x/(1-x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jul 04 2009]
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EXAMPLE
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The a(5)=6 cases are UUUUUDDDDD, UDUUUDUDDD, UDUUUDDUDD, UDUUDUUDDDD, UDUUDUDUDUDD and UUDDUUDUDD
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MAPLE
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A:= proc(n) option remember; if n=0 then 0 else convert (series ((A(n-1)^2 *(x^2-2*x+2) +x)/ (x+1), x, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n): seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 23 2008]
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CROSSREFS
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Cf. A082989.
Adjacent sequences: A035926 A035927 A035928 this_sequence A035930 A035931 A035932
Sequence in context: A022015 A138747 A052975 this_sequence A071646 A114627 A148464
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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).
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EXTENSIONS
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Edited by Lou Shapiro (lshapiro(AT)howard.edu), Feb 16 2005
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