This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023979 #12 Jun 11 2025 09:13:15 %S A023979 0,4,7,11,12,16,17,23,21,23,24,28,27,33,36,37,33,38,37,42,41,44,46,52, %T A023979 48,51,52,51,50,55,55,60,55,57,61,62,58,64,66,70,65,72,71,78,78,76,78, %U A023979 84,79,81,80,82,82,88,84,86,82,85,88,94,90,98,102,102,93,95,94,100,100,104,103,107,102 %N A023979 Sum of exponents in prime-power factorization of multinomial coefficient M(4n; n,n,n,n). %H A023979 Amiram Eldar, <a href="/A023979/b023979.txt">Table of n, a(n) for n = 0..10000</a> %F A023979 From _Amiram Eldar_, Jun 11 2025: (Start) %F A023979 a(n) = A001222(A008977(n)). %F A023979 a(n) = A022559(4*n) - 4*A022559(n). (End) %t A023979 a[n_] := PrimeOmega[Multinomial[n, n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *) %o A023979 (PARI) a(n) = bigomega((4*n)! / n!^4); \\ _Amiram Eldar_, Jun 11 2025 %Y A023979 Cf. A001222, A008977, A022559. %Y A023979 Cf. A023978, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993. %K A023979 nonn %O A023979 0,2 %A A023979 _Clark Kimberling_ %E A023979 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025