A023819 Sum of exponents in prime-power factorization of C(3n,n).

0, 1, 2, 4, 4, 4, 6, 8, 6, 7, 8, 11, 11, 11, 11, 12, 10, 12, 11, 15, 13, 13, 18, 18, 17, 16, 17, 19, 17, 18, 19, 22, 18, 18, 20, 21, 19, 21, 22, 23, 22, 21, 23, 28, 27, 27, 28, 30, 27, 28, 26, 28, 29, 28, 31, 32, 29, 31, 31, 35, 32, 33, 35, 34, 31, 30, 31, 34, 31, 32, 35, 36, 33, 34, 35, 38, 37, 36, 36

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

Equivalently, sum of exponents of primes in multinomial coefficient M(3n; n,n,n)/C(2n,n).

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A005809, A022559.

Programs

Maple

with(numtheory):(combinat):a:=proc(n) if n=0 then 0 else bigomega(binomial(3*n,n)) fi end: seq(a(n), n=0..78); # Zerinvary Lajos, Apr 11 2008

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[3 n, n]][[All, 2]]], {n, 78}]] (* Ivan Neretin, Nov 02 2017 *)

PARI

a(n) = bigomega(binomial(3*n, n)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A005809(n)).

a(n) = A022559(3*n) - A022559(2*n) - A022559(n). (End)

Extensions

Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, May 31 2008

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