A187358 Catalan trisection: A000108(3*n+1), n>=0.

1, 14, 429, 16796, 742900, 35357670, 1767263190, 91482563640, 4861946401452, 263747951750360, 14544636039226909, 812944042149730764, 45950804324621742364, 2622127042276492108820, 150853479205085351660700, 8740328711533173390046320, 509552245179617138054608572, 29869166945772625950142417512

Offset

0,2

Comments

See the comment under A187357 for the o.g.f.s for the general trisection of a sequence.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = C(3*n+1), n>=0, with C(n) = A000108(n) (Catalan).

O.g.f.: (sqrt(2*sqrt(1+4*x^(1/3)+16*x^(2/3))-(1+8*x^(1/3))) - sqrt(1-4*x^(1/3)))/(6*x^(2/3)).

From Ilya Gutkovskiy, Jan 13 2017: (Start)

E.g.f.: 3F3(1/2,5/6,7/6; 1,4/3,5/3; 64*x).

a(n) ~ 4^(3*n+1)/(3*sqrt(3*Pi)*n^(3/2)). (End)

Sum_{n>=0} a(n)/4^n = 2*sqrt(2*sqrt(3) - 3)/3. - Amiram Eldar, Mar 16 2022

a(n) = Product_{1 <= i <= j <= 3*n} (3*i + j + 2)/(3*i + j - 1). - Peter Bala, Feb 22 2023

Mathematica

Table[CatalanNumber[3*n+1], {n, 0, 20}] (* Amiram Eldar, Mar 16 2022 *)

Crossrefs

Cf. A000108, A024492, A048990, A187357 (C(3*n)), A187359 (C(3*n+2)).

Sequence in context: A258392 A269504 A033815 * A103916 A201546 A305115

Adjacent sequences: A187355 A187356 A187357 * A187359 A187360 A187361

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 09 2011

Status

approved