Search: id:A098331
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%I A098331
%S A098331 1,1,1,5,5,11,41,29,125,365,131,1409,3301,155,15625,29485,16115,170035,
%T A098331 254525,309775,1813055,2064655,4617755,18909175,14903725,61552739,
%U A098331 192390589,81290561,767919595,1901796395,28588201
%V A098331 1,1,-1,-5,-5,11,41,29,-125,-365,-131,1409,3301,-155,-15625,-29485,16115,
               170035,254525,
%W A098331 -309775,-1813055,-2064655,4617755,18909175,14903725,-61552739,-192390589,
               -81290561,
%X A098331 767919595,1901796395,28588201
%N A098331 Expansion of 1/sqrt(1-2x+5x^2).
%C A098331 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,...).
%C A098331 Hankel transform is 2^n*(-1)^C(n+1,2). Hankel transform of 0,1,1,-1,-5,
               -5,... is F(n)*(-1)^C(n+2,2)*(2^n+0^n)/2. [From Paul Barry (pbarry(AT)wit.ie), 
               Jan 13 2009]
%D A098331 Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%H A098331 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrinomialCoefficient.html">Trinomial Coefficient</a>
%F A098331 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)}.
%F A098331 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
%t A098331 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)
%Y A098331 Sequence in context: A141244 A121849 A164930 this_sequence A061391 A123133 
               A122213
%Y A098331 Adjacent sequences: A098328 A098329 A098330 this_sequence A098332 A098333 
               A098334
%K A098331 easy,sign
%O A098331 0,4
%A A098331 Paul Barry (pbarry(AT)wit.ie), Sep 03 2004
%E A098331 Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 19 2005

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