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 A001459 a(n) = (5*n)!/((2*n)!*(2*n)!*n!). 3
 1, 30, 3150, 420420, 62355150, 9816086280, 1605660228900, 269764879032000, 46225898052627150, 8042050347997165500, 1415997888807961859400, 251762943910387780962000, 45125969443194371927422500, 8143514687130622653091029120, 1478138194032735032800001630400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS James Spahlinger, Table of n, a(n) for n = 0..400 Romeo Meštrović, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011. FORMULA From Ilya Gutkovskiy, Feb 07 2017: (Start) O.g.f.: 4F3(1/5,2/5,3/5,4/5; 1/2,1/2,1; 3125*x/16). E.g.f.: 4F4(1/5,2/5,3/5,4/5; 1/2,1/2,1,1; 3125*x/16). a(n) ~ 5^(5*n+1/2)/(4*Pi*16^n*n). (End) From Peter Bala, Sep 20 2021: (Start) a(n) = 5*(5*n - 1)*(5*n - 2)*(5*n - 3)*(5*n - 4)/(4*n^2*(2*n - 1)^2)*a(n-1). a(n) = Sum_{k = n..3*n} binomial(3*n,k)^2*binomial(k,n). Cf. A006480. Congruences: a(n*p^k) == a(n*p^(k-1)) ( mod p^(3*k) ) for any prime p >= 5 and any positive integers n and k (write a(n) as C(5*n,2*n)*C(3*n,n) and apply Mestrovic, equation 39, p. 12). (End) MAPLE f := n->(5*n)!/((2*n)!*(2*n)!*n!); MATHEMATICA Table[(5 n)!/((2 n)! (2 n)!*n!), {n, 0, 12}] (* Michael De Vlieger, Feb 07 2017 *) CROSSREFS Cf. A006480. Sequence in context: A036363 A230591 A352182 * A303007 A209788 A265855 Adjacent sequences: A001456 A001457 A001458 * A001460 A001461 A001462 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified March 4 11:02 EST 2024. Contains 370528 sequences. (Running on oeis4.)