A004333 -id:A004333 - cp's OEIS frontend

A023829 Sum of exponents in prime-power factorization of C(4n,n-3).

0, 4, 3, 5, 6, 8, 9, 9, 6, 10, 10, 13, 11, 15, 14, 15, 13, 17, 14, 17, 15, 19, 20, 18, 18, 21, 19, 21, 17, 24, 23, 26, 22, 26, 25, 25, 24, 28, 27, 26, 25, 28, 27, 29, 26, 31, 31, 33, 29, 34, 28, 31, 30, 33, 33, 32, 30, 34, 35, 37, 34, 42, 41, 41, 37, 40, 38, 42, 37, 44, 42, 41, 42, 45, 45, 46, 43, 45

Offset: 3

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 3..10000

Cf. A001222, A004333, A023826, A023827, A023828, A023830, A023831, A023832, A023833, A023834, A023835, A023836.

Table[PrimeOmega[Binomial[4 n, n - 3]], {n, 3, 78}] (* Ivan Neretin, Nov 02 2017 *)

a(n) = bigomega(binomial(4*n,n-3)); \\ Amiram Eldar, Jun 13 2025

From Amiram Eldar, Jun 13 2025 (Start)
a(n) = A001222(A004333(n)).
a(n) = A023828(n) - A001222(3*n+3) + A001222(n-2). (End)

Offset corrected to 3 by Ivan Neretin, Nov 02 2017

A026020 a(n) = binomial(4n, n) - binomial(4n, n - 3).

Original entry on oeis.org

1, 4, 28, 219, 1804, 15314, 132572, 1163565, 10316924, 92195488, 829016968, 7492106505, 67991427828, 619193535380, 5655829748520, 51794730347745, 475390078267356, 4371917301657488, 40276635724273936, 371630891401943020, 3433826368544377520, 31768260456301092090

Offset: 0

Clark Kimberling

G. C. Greubel, Table of n, a(n) for n = 0..1000

a(n) = T(4n, n), where T is the array defined in A026009.
Bisections are A026012 and A026016.
Cf. A004333, A005810.

[Binomial(4*n, n) - Binomial(4*n, n-3): n in [0..20]]; // G. C. Greubel, Mar 22 2021

A026020:= n-> binomial(4*n,n) - binomial(4*n,n-3); seq(A026020(n), n=0..20); # G. C. Greubel, Mar 22 2021

Table[Binomial[4n, n] - Binomial[4n, n - 3], {n, 0, 19}] (* Alonso del Arte, Jun 06 2019 *)

a(n) = binomial(4*n, n) - binomial(4*n, n-3) \\ Felix Fröhlich, Jun 06 2019

[binomial(4*n, n) - binomial(4*n, n-3) for n in (0..20)] # G. C. Greubel, Mar 22 2021

G.f.: (g - 2)*(1 - g + g^2)*g/(3*g - 4) where g = 1 + x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011
a(n) = A005810(n) - A004333(n) for n > 2 - Felix Fröhlich, Jun 06 2019
a(n) ~ 13 * 2^(8*n+3/2) / (3^(3*n+7/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 06 2025

cp's OEIS Frontend

A023829 Sum of exponents in prime-power factorization of C(4n,n-3).

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