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Search: id:A098333
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| A098333 |
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Expansion of 1/sqrt(1-2x+13x^2). |
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+0
3
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| 1, 1, -5, -17, 19, 211, 181, -2015, -5837, 12259, 91585, 29965, -1033955, -2347955, 7953115, 43864543, -11941037, -559875245, -942036911, 5060812717, 21502740649, -20676139991, -307241918945, -344022187613
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Central coefficients of (1+x-3x^2)^n. Binomial transform of 1/sqrt(1+12x^2), or (1,0,-6,0,54,0,-540,...). Binomial transform is A012000.
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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(x)BesselI(0, 2sqrt(-3)x); a(n)=sum{k=0..floor(n/2), binomial(n, 2k)binomial(2k, k)(-3)^k}; a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)(-3)^k).
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CROSSREFS
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Adjacent sequences: A098330 A098331 A098332 this_sequence A098334 A098335 A098336
Sequence in context: A038964 A019401 A153320 this_sequence A162862 A043338 A023711
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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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