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A187358 Catalan trisection: A000108(3*n+1), n>=0. 3
1, 14, 429, 16796, 742900, 35357670, 1767263190, 91482563640, 4861946401452, 263747951750360, 14544636039226909, 812944042149730764, 45950804324621742364, 2622127042276492108820, 150853479205085351660700, 8740328711533173390046320, 509552245179617138054608572, 29869166945772625950142417512 (list; graph; refs; listen; history; text; internal format)
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)

CROSSREFS

Cf. A000108, A024492, 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

AUTHOR

Wolfdieter Lang, Mar 09 2011

STATUS

approved

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Last modified June 12 16:55 EDT 2021. Contains 344959 sequences. (Running on oeis4.)