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A098334
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Expansion of 1/sqrt(1-2x+17x^2).
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2
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1, 1, -7, -23, 49, 401, 41, -5767, -11423, 65569, 299353, -441847, -5511791, -3665999, 79937417, 212712857, -861871423, -5076450239, 3966949049, 89482678313, 110424995569, -1233175514671, -4202194115863
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Central coefficients of (1+x-4x^2)^n. Binomial transform of 1/sqrt(1+16x^2), or (1,0,-8,0,96,0,-1280,...) Binomial transform is A098337.
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REFERENCES
| Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
| E.g.f. : exp(x)BesselI(0, 4*I*x), I=sqrt(-1); a(n)=sum{k=0..floor(n/2), binomial(n, 2k)binomial(2k, k)(-4)^k}; a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)(-4)^k); a(n)=sum{k=0..n, binomial(n, k)binomial(k, k/2)cos(pi*k/2)2^k}3
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CROSSREFS
| Sequence in context: A180044 A062725 A147121 * A038796 A004068 A022815
Adjacent sequences: A098331 A098332 A098333 * A098335 A098336 A098337
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 03 2004
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