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%I #30 Sep 08 2022 08:45:49
%S 1,10,190,4060,91390,2118760,50063860,1198774720,28987537150,
%T 706252528630,17310309456440,426342151127100,10542859559688820,
%U 261594860525768000,6509613950241656640,162392216278033616560,4059949873964357469950,101696990867999141755140
%N a(n) = binomial(10*n, n).
%H Vincenzo Librandi, <a href="/A169959/b169959.txt">Table of n, a(n) for n = 0..115</a>
%F a(n) = C(10*n-1, n-1)*C(100*n^2, 2)/(3*n*C(10*n+1, 3)), n > 0. - _Gary Detlefs_, Jan 02 2014
%F From _Peter Bala_, Feb 21 2022: (Start)
%F The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 9*A(x))^9 + (10^10)*x*A(x)^10 = 0.
%F Sum_{n >= 1} a(n)*( x*(9*x + 10)^9/(10^10*(1 + x)^10) )^n = x. (End)
%o (Magma) [Binomial(10*n, n): n in [0..50]]; // _Vincenzo Librandi_, Apr 21 2011
%Y binomial(k*n,n): A000984 (k = 2), A005809 (k = 3), A005810 (k = 4), A001449 (k = 5), A004355 (k = 6), A004368 (k = 7), A004381 (k = 8), A169958 - A169961 (k = 9 thru 12).
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Aug 07 2010
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