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 A370056 a(n) = 2*(4*n+1)!/(3*n+2)!. 3
 1, 2, 18, 312, 8160, 287280, 12751200, 684028800, 43062243840, 3113350732800, 254265345734400, 23153103246873600, 2326025084653670400, 255579097716214272000, 30491180727539051520000, 3925248256199788277760000, 542357159056633603178496000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..16. FORMULA E.g.f.: exp( 1/2 * Sum_{k>=1} binomial(4*k,k) * x^k/k ). a(n) = A000142(n) * A069271(n). D-finite with recurrence 3*(3*n+2)*(3*n+1)*a(n) -8*(4*n+1)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Feb 22 2024 PROG (PARI) a(n) = 2*(4*n+1)!/(3*n+2)!; CROSSREFS Cf. A365340, A370057, A370058. Cf. A000142, A069271. Sequence in context: A192555 A370941 A350366 * A179497 A296837 A326270 Adjacent sequences: A370053 A370054 A370055 * A370057 A370058 A370059 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 08 2024 STATUS approved

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Last modified May 27 20:38 EDT 2024. Contains 372882 sequences. (Running on oeis4.)