A023980 Sum of exponents in prime-power factorization of multinomial coefficient M(4n;2n,n,n).

0, 3, 5, 8, 9, 11, 12, 17, 15, 17, 18, 20, 20, 24, 25, 26, 24, 27, 26, 30, 29, 32, 34, 37, 35, 37, 37, 37, 36, 39, 40, 44, 40, 41, 45, 45, 43, 48, 48, 51, 48, 51, 51, 56, 56, 55, 56, 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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A000897, A022559.

Cf. A023978, A023979, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Multinomial[2*n, n, n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)

PARI

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

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A000897(n)).

a(n) = A022559(4*n) - A022559(2*n) - 2*A022559(n). (End)

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025