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A023982 Sum of exponents in prime-power factorization of multinomial coefficient M(5n;3n,n,n).

%I A023982 #10 Jun 11 2025 09:13:34
%S A023982 0,3,6,7,9,13,13,17,17,17,19,21,20,27,27,28,26,30,29,30,34,36,33,38,
%T A023982 36,38,43,40,40,46,44,48,43,46,47,48,47,51,53,55,53,57,57,55,57,59,58,
%U A023982 63,58,62,63,64,67,73,66,69,68,67,73,73,74,79,80,78,71,77,76,77,79,84,79,87,82,87,89,86,89
%N A023982 Sum of exponents in prime-power factorization of multinomial coefficient M(5n;3n,n,n).
%H A023982 Amiram Eldar, <a href="/A023982/b023982.txt">Table of n, a(n) for n = 0..10000</a>
%F A023982 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023982 a(n) = A001222(A001451(n)).
%F A023982 a(n) = A022559(5*n) - A022559(3*n) - 2*A022559(n). (End)
%t A023982 a[n_] := PrimeOmega[Multinomial[3*n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023982 (PARI) a(n) = bigomega((5*n)! / ((3*n)!*n!*n!)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023982 Cf. A001222, A001451, A022559.
%Y A023982 Cf. A023978, A023979, A023980, A023981, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023982 nonn
%O A023982 0,2
%A A023982 _Clark Kimberling_
%E A023982 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025