A187366 One half of a trisection of A001700: binomial(6n+5,3(n+1))/2, n>=0.

5, 231, 12155, 676039, 38779380, 2268783825, 134564468610, 8061900920775, 486734856412028, 29566145391215356, 1804857108504066435, 110628135069209194801, 6804253717299758003900, 419727621552972772561830, 25956855321888352842417780

Offset: 0

Author

Wolfdieter Lang, Mar 10 2011

Keywords

• nonn
• easy

Comments

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

Crossrefs

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

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

Formula

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

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),

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).