A187366 - OEIS

%I #4 Mar 30 2012 18:49:34

%S 5,231,12155,676039,38779380,2268783825,134564468610,8061900920775,

%T 486734856412028,29566145391215356,1804857108504066435,

%U 110628135069209194801,6804253717299758003900,419727621552972772561830,25956855321888352842417780

%N One half of a trisection of A001700: binomial(6n+5,3(n+1))/2, n>=0.

%C For trisection of a sequence see a comment and a reference under A187357.

%F a(n)= binomial(2*(3*n+2)+1,(3*n+2)+1)/2 = binomial(6*n+5,3*(n+1))/2 , n>=0.

%F O.g.f.: (cb(x^(1/3)) - 3 + sqrt(2)*P(x^(1/3))*sqrt(1/P(x^(1/3)) + 1 + 2*x^(1/3)))/(12*x),

%F with cb(x):=1/sqrt(1-4*x) (o.g.f. of A000984) and P(x):=P(-1/2,4*x)=1/sqrt(1+4*x+16*x^2) (o.g.f. of A116091, with P(x,z)the o.g.f. of the Legendre polynomials).

%Y Cf. A187364 binomial(2(3n)+1,3n+1),

%Y A187365 binomial(2(3n+1)+1,(3n+1)+1)/3.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Mar 10 2011