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Search: id:A098337
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| A098337 |
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Expansion of 1/sqrt(1-4x+20x^2). |
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+0
3
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| 1, 2, -4, -40, -80, 352, 2624, 3712, -32000, -186880, -134144, 2885632, 13520896, -1269760, -256000000, -966164480, 1056112640, 22286827520, 66722201600, -162411315200, -1901125959680, -4329895362560
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Central coefficients of (1+2x-4x^2)^n. Binomial transform of A098334.
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REFERENCES
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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
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E.g.f. :exp(2x)BesselI(0, 4*I*x), I=sqrt(-1); a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)2^n(-1)^k}; a(n)=sum{k=0..n, binomial(2k, k)binomial(k, n-k)(-5)^(n-k)}.
a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(2(n-k), n)(-5)^k} - Paul Barry (pbarry(AT)wit.ie), Sep 08 2004
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CROSSREFS
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Sequence in context: A098625 A057777 A139735 this_sequence A158213 A012596 A012676
Adjacent sequences: A098334 A098335 A098336 this_sequence A098338 A098339 A098340
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 03 2004
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