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, 1608766753466574727105400775

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..15.

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).

a(n) ~ 4(3*n+2) / sqrt(3*Pi*n). - Amiram Eldar, Oct 16 2025

Mathematica

a[n_] := Binomial[6*n+5, 3*(n+1)]/2; Array[a, 20, 0] (* Amiram Eldar, Oct 16 2025 *)

Crossrefs

Cf. A000984, A001700, A116091, A187357, A187364 (binomial(2(3n)+1,3n+1)), A187365 (binomial(2(3n+1)+1,(3n+1)+1)/3).

Sequence in context: A065757 A157776 A147540 * A176898 A274996 A142668

Adjacent sequences: A187363 A187364 A187365 * A187367 A187368 A187369

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 10 2011

Status

approved