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A023985 Sum of exponents in prime-power factorization of multinomial coefficient M(6n,2n,2n,2n).

%I A023985 #9 Jun 11 2025 09:13:53
%S A023985 0,4,7,11,12,14,18,22,19,22,25,30,30,32,31,34,33,36,34,40,39,43,49,50,
%T A023985 49,49,51,54,51,54,57,63,56,56,60,63,61,67,67,68,67,67,70,77,76,77,80,
%U A023985 83,78,81,79,84,85,84,88,93,89,93,95,99,95,99,102,100,94,95,98,102,98,101,105,109,104
%N A023985 Sum of exponents in prime-power factorization of multinomial coefficient M(6n,2n,2n,2n).
%H A023985 Amiram Eldar, <a href="/A023985/b023985.txt">Table of n, a(n) for n = 0..10000</a>
%F A023985 a(n) = A022559(6*n) - 3*A022559(2*n). - _Amiram Eldar_, Jun 11 2025
%t A023985 a[n_] := PrimeOmega[Multinomial[2*n, 2*n, 2*n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023985 (PARI) a(n) = bigomega((6*n)! / ((2*n)!)^3); \\ _Amiram Eldar_, Jun 11 2025
%Y A023985 Cf. A001222, A022559.
%Y A023985 Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023985 nonn
%O A023985 0,2
%A A023985 _Clark Kimberling_
%E A023985 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025