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Search: id:A082181
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| A082181 |
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a(0)=1, for n>=1 a(n)=sum(k=0,n,9^k*N(n,k)) where N(n,k) =1/n*C(n,k)*C(n,k+1) are the Narayana numbers (A001263). |
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+0
7
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| 1, 1, 10, 109, 1270, 15562, 198100, 2596645, 34825150, 475697854, 6595646860, 92590323058, 1313427716380, 18798095833012, 271118225915560, 3936516861402901, 57494017447915150, 844109420603623030
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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More generally coefficients of (1+m*x-sqrt(m^2*x^2-(2*m+4)*x+1))/((2*m+2)*x) are given by : a(n)=sum(k=0,n,(m+1)^k*N(n,k))
The Hankel transform of this sequence is 9^C(n+1,2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
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REFERENCES
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Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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FORMULA
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G.f. (1+8*x-sqrt(64*x^2-20*x+1))/(18*x)
a(n) = Sum_{k=0..n} A088617(n, k)*9^k*(-8)^(n-k) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 21 2004
a(n) = [10(2n-1)a(n-1) - 64(n-2)a(n-2)] / (n+1) for n>=2, a(0) = a(1) = 1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 19 2005
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PROGRAM
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(PARI) a(n)=if(n<1, 1, sum(k=0, n, 9^k/n*binomial(n, k)*binomial(n, k+1)))
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CROSSREFS
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Cf. A001003, A007564, A059231.
Sequence in context: A024527 A015591 A078922 this_sequence A095740 A075508 A095176
Adjacent sequences: A082178 A082179 A082180 this_sequence A082182 A082183 A082184
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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