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Search: id:A081178
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| A081178 |
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a(0)=1, for n>=1 a(n)=sum(k=0,n,7^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, 8, 71, 680, 6882, 72528, 788019, 8766248, 99362894, 1143498224, 13326176998, 156950554384, 1865210341828, 22338852956064, 269355965364459, 3267146912972328, 39837475762660374, 488032452193307568
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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 7^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+6*x-sqrt(36*x^2-16*x+1))/(14*x)
a(n) = [8(2n-1)a(n-1) - 36(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, 7^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: A038145 A015576 A070998 this_sequence A096341 A075506 A094911
Adjacent sequences: A081175 A081176 A081177 this_sequence A081179 A081180 A081181
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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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