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

4,1

Comments

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

Links

Table of n, a(n) for n=4..17.

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A268512, A087754, A268590.

Sequence in context: A129206 A135398 A203426 * A372343 A228289 A306391

Adjacent sequences: A268586 A268587 A268588 * A268590 A268591 A268592

Keyword

nonn

Author

Max Alekseyev, Feb 07 2016

Status

approved