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 A187364 Trisection of A000984 (central binomial coefficients): binomial(2(3n+1),3n+1)/2, n>=0. 8
 1, 35, 1716, 92378, 5200300, 300540195, 17672631900, 1052049481860, 63205303218876, 3824345300380220, 232714176627630544, 14226520737620288370, 873065282167813104916, 53753604366668088230810, 3318776542511877736535400, 205397724721029574666088520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See a comment under A187363 concerning trisection. This appears also in the trisection of A001700 (central binomials in the odd numbered Pascal rows):  binomial(2*(3*n)+1,3*n+1). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..554 FORMULA a(n)=binomial(2*(3*n+1),3*n+1)/2, n>=0. a(n)=binomial(2*(3*n)+1,3*n+1), n>=0. O.g.f.: (cb(x^(1/3)) - sqrt(2)*P(x^(1/3))*sqrt(1/P(x^(1/3))-(1+8*x^(1/3))/2))/(6*x^(1/3)), 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). MATHEMATICA Table[c=3n+1; Binomial[2c, c]/2, {n, 0, 20}] (* Harvey P. Dale, May 10 2012 *) CROSSREFS A066802 binomial(6n,3n), A187365 binomial(2(3n+2),3n+2)/3!. Sequence in context: A180883 A130005 A199362 * A183417 A199587 A001825 Adjacent sequences:  A187361 A187362 A187363 * A187365 A187366 A187367 KEYWORD nonn AUTHOR Wolfdieter Lang, Mar 10 2011 STATUS approved

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Last modified September 20 12:05 EDT 2021. Contains 347586 sequences. (Running on oeis4.)