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A082366
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G.f.: (1-7*x-sqrt(49*x^2-18*x+1))/(2*x).
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3
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1, 8, 72, 712, 7560, 84616, 985032, 11814728, 145043208, 1813915912, 23029334856, 296050614216, 3846007927944, 50412893051784, 665925356663496, 8855844075949128, 118467982501096968, 1593108078166843912
(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 8^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, 8^k*C(n, k)*C(n, k-1)).
Conjecture: (n+1)*a(n)+9*(1-2n)*a(n-1)+49*(n-2)*a(n-2)=0. - R. J. Mathar, Dec 08 2011
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MATHEMATICA
| CoefficientList[Series[(1-7x-Sqrt[49x^2-18x+1])/(2x), {x, 0, 20}], x] (* From Harvey P. Dale, Feb 22 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 1, sum(k=0, n, 8^k*binomial(n, k)*binomial(n, k-1))/n)
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CROSSREFS
| Cf. A006318, A047891.
Sequence in context: A145303 A098411 A165323 * A049388 A014479 A013992
Adjacent sequences: A082363 A082364 A082365 * A082367 A082368 A082369
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
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