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A187365 Trisection of A000984 (central binomial coefficients): binomial(2(3n+2),3n+2)/3!, n>=0. 6
1, 42, 2145, 117572, 6686100, 388934370, 22974421470, 1372238454600, 82653088824684, 5011211083256840, 305437356823765089, 18697712969443807572, 1148770108115543559100, 70797430141465286938140, 4374750896947475198160300, 270950190057528375091435920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See a comment under A187357 concerning trisection.

This appears also in the trisection of A001700: binomial(2*(3*n+1)+1,(3*n+1)+1)/3.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..554

FORMULA

a(n)=binomial(2*(3*n+2),3*n+2)/3!, n>=0.

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

O.g.f.:(cb(x^(1/3)) - sqrt(2)*P(x^(1/3))*sqrt(1/P(x^(1/3))-(1-4*x^(1/3))/2))/(18*x^(2/3)),

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).

CROSSREFS

Cf. A066802 binomial(6n,3n).

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

Sequence in context: A236270 A216703 A258393 * A294978 A180371 A046198

Adjacent sequences:  A187362 A187363 A187364 * A187366 A187367 A187368

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Mar 10 2011

STATUS

approved

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Last modified September 23 19:03 EDT 2021. Contains 347617 sequences. (Running on oeis4.)