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 A023991 #10 Jun 11 2025 09:14:23 %S A023991 1,4,6,8,8,12,12,13,13,15,17,20,19,22,21,22,21,24,25,26,25,31,30,32, %T A023991 30,31,33,33,32,36,34,36,34,36,36,37,36,40,40,42,40,45,48,49,49,51,50, %U A023991 52,49,50,50,53,50,56,53,53,53,55,58,60,59,62,60,60,55,58,59,61,60,65,62,65,63,66,69,68 %N A023991 Sum of exponents of primes in multinomial coefficient M(3n; n+1,n,n-1). %H A023991 Amiram Eldar, <a href="/A023991/b023991.txt">Table of n, a(n) for n = 1..10000</a> %F A023991 From _Amiram Eldar_, Jun 11 2025: (Start) %F A023991 a(n) = A001222(A248707(n)). %F A023991 a(n) = A022559(3*n) - A022559(n-1) - A022559(n) - A022559(n+1) = A022559(3*n) - 3*A022559(n) - A001222(n+1) + A001222(n) = A023978(n) - A076191(n). (End) %t A023991 a[n_] := PrimeOmega[Multinomial[n+1, n, n-1]]; Array[a, 100] (* _Amiram Eldar_, Jun 11 2025 *) %o A023991 (PARI) a(n) = bigomega((3*n)! / ((n-1)!*n!*(n+1)!)); \\ _Amiram Eldar_, Jun 11 2025 %Y A023991 Cf. A001222, A022559, A023978, A076191, A248707. %Y A023991 Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023992, A023993. %K A023991 nonn %O A023991 1,2 %A A023991 _Clark Kimberling_