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Search: id:A098331
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| A098331 |
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Expansion of 1/sqrt(1-2x+5x^2). |
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+0
7
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| 1, 1, -1, -5, -5, 11, 41, 29, -125, -365, -131, 1409, 3301, -155, -15625, -29485, 16115, 170035, 254525, -309775, -1813055, -2064655, 4617755, 18909175, 14903725, -61552739, -192390589, -81290561, 767919595, 1901796395, 28588201
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Central coefficients of (1+x-x^2)^n. Binomial transform of 1/sqrt(1+4x^2), or (1,0,-2,0,6,0,-20,...). Binomial transform is A098335. (-1)^nA098331(n) is the inverse binomial transform of (1,0,-2,0,6,0,-20,...).
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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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LINKS
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Eric Weisstein's World of Mathematics, Trinomial Coefficient
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FORMULA
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E.g.f. : exp(x)BesselI(0, 2*I*x), I=sqrt(-1); a(n)=sum{k=0..floor(n/2), binomial(n, 2k)binomial(2k, k)(-1)^k}; a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)(-1)^k); a(n)=sum{k=0..n, binomial(n, k)binomial(k, k/2)cos(pi*k/2)}.
a(0)=a(1)=1, a(n)=((2n-1)a(n-1)-5(n-1)a(n-2))/n - T. D. Noe (noe(AT)sspectra.com), Oct 19 2005
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MATHEMATICA
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a=b=1; Join[{a, b}, Table[c=((2n-1)b-5(n-1)a)/n; a=b; b=c; c, {n, 2, 30}]] (Noe)
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CROSSREFS
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Adjacent sequences: A098328 A098329 A098330 this_sequence A098332 A098333 A098334
Sequence in context: A101203 A141244 A121849 this_sequence A061391 A123133 A122213
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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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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 19 2005
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