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Search: id:A086616
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| 1, 3, 9, 31, 121, 515, 2321, 10879, 52465, 258563, 1296281, 6589727, 33887465, 175966211, 921353249, 4858956287, 25786112993, 137604139011, 737922992937, 3974647310111, 21493266631001, 116642921832963, 635074797251889
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OFFSET
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0,2
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COMMENT
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Partial sums of the sequence of the large Schroeder numbers (A006318). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 20 2004
Hankel transform is A136577(n+1). [From Paul Barry (pbarry(AT)wit.ie), Jun 03 2009]
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FORMULA
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G.f.: A(x) = 1/(1-x)^2 + x*A(x)^2.
a(1)=1, a(n)=n+sum(i=1, n-1, a(i)*a(n-i)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 16 2004
G.f.: [1-x-sqrt(1-6x+x^2)]/[2x(1-x)]. Cf. A001003. - R. Stephan, Mar 23 2004
a(n)=sum{k=0..n, C(n+k+1,2k+1)*A000108(k)}. [From Paul Barry (pbarry(AT)wit.ie), Jun 03 2009]
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EXAMPLE
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a(1)=2+1=3, a(2)=3+4+2=9, a(3)=4+10+12+5=31, a(4)=5+20+42+40+14=121.
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CROSSREFS
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Cf. A086614 (triangle), A086615 (antidiagonal sums).
Cf. A006318.
Sequence in context: A151037 A066571 A087648 this_sequence A040027 A071603 A090595
Adjacent sequences: A086613 A086614 A086615 this_sequence A086617 A086618 A086619
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003
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