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Search: id:A046748
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| A046748 |
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Expansion of sqrt(1-4*x)/(1-5*x); row sums of triangle A046521. |
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+0
5
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| 1, 3, 13, 61, 295, 1447, 7151, 35491, 176597, 880125, 4390901, 21920913, 109486993, 547018941, 2733608905, 13662695645, 68294088535, 341399727335, 1706739347095, 8532741458075, 42660172763995, 213287735579135
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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i)Homogeneous recursion: a(n) = (3*(3*n-2)/n)*a(n-1) - (10*(2*n-3)/n)*a(n-2), n >= 1, a(-1) := 0, a(0)=1. ii) Hypergeometric 2F1 form: a(n)=binomial(2*n,n)*hypergeom([ -n,1 ],[ 1/2 ],-1/4).
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FORMULA
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a(n) = binomial(2*n, n)*sum(binomial(n, k)/binomial(2*k, k), k=0..n) = 5^n - 2*A046714(n-1), A046714(-1) := 0; a(n) = 5*a(n-1) - 2*A000108(n-1), A000108(n): Catalan; G.f. sqrt(1-4*x)/(1-5*x).
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CROSSREFS
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A046521, A046714, A000108.
Sequence in context: A108143 A101368 A026704 this_sequence A074548 A141786 A122122
Adjacent sequences: A046745 A046746 A046747 this_sequence A046749 A046750 A046751
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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