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 A320920 a(n) is the smallest number m such that binomial(m,n) is nonzero and is divisible by n!. 1
 1, 4, 9, 33, 28, 165, 54, 1029, 40832, 31752, 28680, 2588680, 2162700, 12996613, 12341252, 4516741125, 500367376, 133207162881, 93770874890, 7043274506259 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is such that a nontrivial n-symmetric permutation of [1..a(n)] might exist. LINKS Tanya Khovanova, 3-Symmetric Permutations EXAMPLE The sequence of binomial coefficients C(n,3) starts as: 0, 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, and so on. The smallest nonzero number divisible by 3! is 84, which is C(9,3). Therefore a(3) = 9. PROG (Python) from sympy import factorial, binomial def A320920(n):     w, m = int(factorial(n)), n     bc = [int(binomial(n-1, i)) % w for i in range(n+1)]     while True:         bc[n] = (bc[n-1]+bc[n]) % w         if bc[n] == 0:             return m         for i in range(n-1, 0, -1):             bc[i] = (bc[i-1]+bc[i]) % w         m += 1 # Chai Wah Wu, Oct 25 2018 CROSSREFS Cf. A042948, A316775, A320919. Sequence in context: A129196 A119574 A006393 * A048757 A173659 A054433 Adjacent sequences:  A320917 A320918 A320919 * A320921 A320922 A320923 KEYWORD nonn,more AUTHOR Tanya Khovanova, Oct 24 2018 EXTENSIONS a(14)-a(15) from Alois P. Heinz, Oct 24 2018 a(16)-a(17) from Chai Wah Wu, Oct 25 2018 a(18)-a(19) from Giovanni Resta, Oct 26 2018 a(20) from Giovanni Resta, Oct 27 2018 STATUS approved

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Last modified January 23 02:40 EST 2019. Contains 319365 sequences. (Running on oeis4.)