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Search: id:A082302
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| A082302 |
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G.f.: (1-5*x-sqrt(25*x^2-14*x+1))/(2*x). |
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+0
4
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| 1, 6, 42, 330, 2814, 25422, 239442, 2326434, 23151030, 234784662, 2417832186, 25216231866, 265796560302, 2827138163550, 30306009654690, 327081253546770, 3551148743559270, 38758882760119590, 425024567305557450
(list; graph; listen)
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OFFSET
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0,2
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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*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))
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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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a(0)=1, n>0 a(n)=(1/n)*sum(k=0, n, 6^k*C(n, k)*C(n, k-1))
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PROGRAM
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(PARI) a(n)=if(n<1, 1, sum(k=0, n, 6^k*binomial(n, k)*binomial(n, k-1))/n)
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CROSSREFS
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Cf. A006318, A047891.
Equals 6*A078018(n) for n>0.
Sequence in context: A107266 A118351 A033296 this_sequence A029588 A001725 A123510
Adjacent sequences: A082299 A082300 A082301 this_sequence A082303 A082304 A082305
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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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