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A082367
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G.f.: (1-8*x-sqrt(64*x^2-20*x+1))/(2*x).
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3
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1, 9, 90, 981, 11430, 140058, 1782900, 23369805, 313426350, 4281280686, 59360821740, 833312907522, 11820849447420, 169182862497108, 2440064033240040, 35428651752626109, 517446157031236350
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| More generally coefficients of (1-m*x-sqrt(m^2*x^2-(2*m+4)*x+1))/(2*x) are given by a(0)=1 and n>0 a(n)=(1/n)*sum(k=0,n,(m+1)^k*C(n,k)*C(n,k-1))
Hankel transform is 9^C(n+1,2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 11 2009]
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REFERENCES
| 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
| a(0)=1, n>0 a(n)=(1/n)*sum(k=0, n, 9^k*C(n, k)*C(n, k-1)).
Conjecture: (n+1)*a(n)+10*(1-2n)*a(n-1)+64*(n-2)*a(n-2)=0. - R. J. Mathar, Dec 08 2011
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PROG
| (PARI) a(n)=if(n<1, 1, sum(k=0, n, 9^k*binomial(n, k)*binomial(n, k-1))/n)
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CROSSREFS
| Cf. A006318, A047891.
Sequence in context: A098399 A143079 A165324 * A049389 A127769 A062815
Adjacent sequences: A082364 A082365 A082366 * A082368 A082369 A082370
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
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