A268590 a(n) = (3*C(4p,p) - 20*C(3p,p) + 54*C(2p,p) - 60) / p^7, where p = prime(n).

984, 27780, 32144568, 1269360060, 2470299005220, 316528131552725460, 17262503097511844124, 3329177348896984023277536, 12461979236231507288981559840, 783882118494853605112684502280, 3251723952081272231067929776337100, 959689034437453143807696476144553320100

Offset: 5

Author

Max Alekseyev, Feb 07 2016

Keywords

• nonn

Comments

a(n) is an integer for all n>=5, 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, A268589.

Programs

PARI

{ A268590(n) = my(p=prime(n)); (-60 + 54*binomial(2*p,p) - 20*binomial(3*p,p) + 3*binomial(4*p,p))/p^7; }