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A023983 Sum of exponents in prime-power factorization of multinomial coefficient M(5n;2n,2n,n).

%I A023983 #10 Jun 11 2025 09:13:34
%S A023983 0,3,6,8,10,12,14,19,17,18,21,24,24,29,27,29,27,31,29,33,35,37,39,41,
%T A023983 40,40,45,45,43,48,48,54,46,48,51,52,51,56,57,59,58,57,60,61,62,65,64,
%U A023983 69,63,68,66,69,74,76,74,78,75,76,81,82,81,85,87,83,77,81,82,84,81,87,86,93,87,91,92,93,96
%N A023983 Sum of exponents in prime-power factorization of multinomial coefficient M(5n;2n,2n,n).
%H A023983 Amiram Eldar, <a href="/A023983/b023983.txt">Table of n, a(n) for n = 0..10000</a>
%F A023983 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023983 a(n) = A001222(A001459(n)).
%F A023983 a(n) = A022559(5*n) - 2*A022559(2*n) - A022559(n). (End)
%t A023983 a[n_] := PrimeOmega[Multinomial[2*n, 2*n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023983 (PARI) a(n) = bigomega((5*n)! / ((2*n)!^2*n!)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023983 Cf. A001222, A001459, A022559.
%Y A023983 Cf. A023978, A023979, A023980, A023981, A023982, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023983 nonn
%O A023983 0,2
%A A023983 _Clark Kimberling_
%E A023983 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025