A268589 a(n) = (2*C(3p,p) - 9*C(2p,p) + 12) / p^5, where p = prime(n).

12, 2364, 43500, 20791626, 514377588, 373783661124, 9888937247184828, 312285010312512084, 11167980739981519994382, 13185583459205473525798038, 462369843775374621687338484, 588608385261717115044847555476, 28758863221144089886068560242560564, 1508365481231852329668720928730586740868

Offset: 4

Author

Max Alekseyev, Feb 07 2016

Keywords

• nonn
• changed

Comments

a(n) is an integer for all n>=4, see A268512.

Links

• R. R. Aidagulov and M. A. Alekseyev. On p-adic approximation of sums of binomial coefficients. Journal of Mathematical Sciences 233:5 (2018), 626-634. doi:10.1007/s10958-018-3948-0; arXiv preprint, arXiv:1602.02632 [math.NT], 2016-2018.

Crossrefs

Cf. A268512, A087754, A268590.

Programs

Mathematica

Table[(2*Binomial[3p,p]-9*Binomial[2p,p]+12)/p^5,{p,Prime[Range[4,20]]}] (* Harvey P. Dale, Aug 27 2025 *)

PARI

{ A268589(n) = my(p=prime(n)); (12 - 9*binomial(2*p,p) + 2*binomial(3*p,p))/p^5; }