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 A023980 #11 Jun 11 2025 09:13:20 %S A023980 0,3,5,8,9,11,12,17,15,17,18,20,20,24,25,26,24,27,26,30,29,32,34,37, %T A023980 35,37,37,37,36,39,40,44,40,41,45,45,43,48,48,51,48,51,51,56,56,55,56, %U A023980 60,57,59,57,59,60,63,61,63,60,63,65,68,65,71,74,73,68,69,69,73,71,75,75,77,74,78,79,81,81 %N A023980 Sum of exponents in prime-power factorization of multinomial coefficient M(4n;2n,n,n). %H A023980 Amiram Eldar, <a href="/A023980/b023980.txt">Table of n, a(n) for n = 0..10000</a> %F A023980 From _Amiram Eldar_, Jun 11 2025: (Start) %F A023980 a(n) = A001222(A000897(n)). %F A023980 a(n) = A022559(4*n) - A022559(2*n) - 2*A022559(n). (End) %t A023980 a[n_] := PrimeOmega[Multinomial[2*n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *) %o A023980 (PARI) a(n) = bigomega((4*n)! / ((2*n)! * n!^2)); \\ _Amiram Eldar_, Jun 11 2025 %Y A023980 Cf. A001222, A000897, A022559. %Y A023980 Cf. A023978, A023979, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993. %K A023980 nonn %O A023980 0,2 %A A023980 _Clark Kimberling_ %E A023980 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025