A023992 Sum of exponents of primes in multinomial coefficient M(4n; n+2,2n,n-2).

3, 7, 9, 11, 11, 15, 15, 19, 18, 19, 21, 24, 22, 25, 26, 28, 26, 29, 29, 34, 33, 34, 36, 38, 35, 38, 38, 39, 38, 41, 42, 44, 43, 44, 46, 49, 45, 50, 50, 52, 51, 54, 55, 58, 55, 56, 58, 61, 57, 60, 60, 61, 60, 63, 62, 66, 64, 66, 67, 71, 68, 70, 72, 73, 70, 72, 70, 76, 74, 75, 77, 79, 76

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001222, A022559.

Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Multinomial[2*n, n+2, n-2]]; Array[a, 100] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega((4*n)! / ((2*n)!*(n-2)!*(n+2)!)); \\ Amiram Eldar, Jun 11 2025

Formula

a(n) = A022559(4*n) - A022559(2*n) - A022559(n+2) - A022559(n-2). - Amiram Eldar, Jun 11 2025

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Jun 17 2019

Offset changed to 2 and a(1) removed by Amiram Eldar, Jun 11 2025