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Search: id:A106260
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| A106260 |
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Expansion of 1/sqrt(1-16x-16x^2). |
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+0
5
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| 1, 8, 104, 1472, 21856, 333568, 5183744, 81590272, 1296426496, 20750839808, 334081306624, 5404163080192, 87763693060096, 1430025994108928, 23367175920287744, 382767375745810432, 6283401962864377856
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OFFSET
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0,2
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COMMENT
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Central coefficient of (1+8x+20x^2)^n. Eighth binomial transform of 1/sqrt(1-80x^2). In general, 1/sqrt(1-4*r*x-4*r*x^2) has e.g.f. exp(2rx)BesselI(0,2r*sqrt((r+1)/r)x)), a(n)=sum{k=0..n, C(2k,k)C(k,n-k)r^k}, gives the central coefficient of (1+(2r)x+r(r+1)x^2), and is the (2r)-th binomial transform of 1/sqrt(1-8*C(n+1,2)x^2).
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FORMULA
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E.g.f.: exp(8*x)*BesselI(0, 8*sqrt(5/4)*x); a(n)=sum{k=0..n, C(2k, k)C(k, n-k)4^k}.
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CROSSREFS
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Cf. A006139, A106258, A106259, A106261.
Sequence in context: A138430 A109774 A001657 this_sequence A112121 A141383 A034300
Adjacent sequences: A106257 A106258 A106259 this_sequence A106261 A106262 A106263
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 28 2005
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