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A023984 Sum of exponents in prime-power factorization of multinomial coefficient M(6n; n,n,n,n,n,n).

%I A023984 #11 Jun 11 2025 09:13:36
%S A023984 0,7,13,20,21,29,33,40,37,40,43,54,51,59,64,67,60,69,67,76,75,79,85,
%T A023984 95,88,91,96,96,93,102,102,111,101,104,108,114,106,115,121,125,118,
%U A023984 130,130,143,142,140,146,155,144,147,148,153,151,159,157,162,155,159,164,177,170,180,186
%N A023984 Sum of exponents in prime-power factorization of multinomial coefficient M(6n; n,n,n,n,n,n).
%H A023984 Amiram Eldar, <a href="/A023984/b023984.txt">Table of n, a(n) for n = 0..10000</a>
%F A023984 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023984 a(n) = A001222(A008979(n)).
%F A023984 a(n) = A022559(6*n) - 6*A022559(n). (End)
%t A023984 a[n_] := PrimeOmega[Multinomial[n, n, n, n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023984 (PARI) a(n) = bigomega((6*n)! / (n!)^6); \\ _Amiram Eldar_, Jun 11 2025
%Y A023984 Cf. A001222, A008979, A022559.
%Y A023984 Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023985, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023984 nonn
%O A023984 0,2
%A A023984 _Clark Kimberling_
%E A023984 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025