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 A188685 Partial alternating sums of binomial(3n,n)^2/(2n+1)^2. 10
 1, 0, 9, 135, 2890, 71639, 1967545, 58125959, 1813561210, 59034994415, 1987910416810, 68818255912790, 2437897047570874, 88061136002276310, 3234416650430634090, 120525771933269446806, 4548292982313797644875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..608 FORMULA a(n) = Sum_{k=0..n} (-1)^(n-k)*A001764(k)^2. 4*(2*n^2 + 9*n + 10)^2*a(n+2) - (713*n^4 + 4230*n^3 + 9317*n^2 + 9000*n + 3200)*a(n+1) - 9*(9*n^2 + 27*n + 20)^2*a(n) = 0. a(n) ~ 3^(6*n+7)/(745*Pi*n^3*2^(4*n+4)). - Vaclav Kotesovec, Aug 06 2013 MAPLE A001764 := proc(n) binomial(3*n, n)/(2*n+1) ; end proc: A188685 := proc(n) add( (-1)^(n-k)*A001764(k)^2, k=0..n) ; end proc: # R. J. Mathar, Apr 11 2011 MATHEMATICA Table[Sum[Binomial[3k, k]^2(-1)^(n-k)/(2k+1)^2, {k, 0, n}], {n, 0, 20}] PROG (Maxima) makelist(sum(binomial(3*k, k)^2*(-1)^(n-k)/(2k+1)^2, k, 0, n), n, 0, 20); (MAGMA) [ &+[(-1)^(n-k)*Binomial(3*k, k)^2/(2*k+1)^2: k in [0..n]]: n in [0..16]];  // Bruno Berselli, Apr 11 2011 CROSSREFS Cf. A001764, A005809, A104859, A188678, A188681. Cf. Alternate partial sums of binomial(3n,n)^2/(2n+1)^k: A188680 (k=0), A188683 (k=1), this sequence (k=2). Sequence in context: A235339 A306848 A034723 * A052137 A003376 A253879 Adjacent sequences:  A188682 A188683 A188684 * A188686 A188687 A188688 KEYWORD nonn,easy AUTHOR Emanuele Munarini, Apr 08 2011 STATUS approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)