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A098332
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Expansion of 1/sqrt(1-2x+9x^2).
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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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, 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
| Sequence in context: A051498 A092528 A069604 * A096663 A133369 A110123
Adjacent sequences: A098329 A098330 A098331 * A098333 A098334 A098335
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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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