0,4

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,...).

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]

Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

Eric Weisstein's World of Mathematics, Trinomial Coefficient

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

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)

Adjacent sequences: A098328 A098329 A098330 this_sequence A098332 A098333 A098334

Sequence in context: A141244 A121849 A164930 this_sequence A061391 A123133 A122213

easy,sign

Paul Barry (pbarry(AT)wit.ie), Sep 03 2004

Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 19 2005