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Search: id:A098332
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| A098332 |
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Expansion of 1/sqrt(1-2x+9x^2). |
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+0
4
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| 1, 1, -3, -11, 1, 81, 141, -363, -1791, -479, 13597, 29877, -54911, -353807, -223443, 2539989, 6806529, -8302527, -73999299, -73313931, 489731841, 1584548241, -1110170163, -15812965611, -21391839999, 94696016481
(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-2x^2)^n. Binomial transform of 1/sqrt(1+8x^2), or (1,0,-4,0,24,0,...). Binomial transform is A098336.
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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(-2)x); a(n)=sum{k=0..floor(n/2), binomial(n, 2k)binomial(2k, k)(-2)^k}; a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)(-2)^k); a(n)=(-1)^n*sum{k=0..n, binomial(n, k)^2*(-2)^k}.
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CROSSREFS
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Sequence in context: A051498 A092528 A069604 this_sequence A096663 A133369 A110123
Adjacent sequences: A098329 A098330 A098331 this_sequence A098333 A098334 A098335
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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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