A087754 a(n) = (C(2p,p)-2) / p^3, where p = prime(n).

2, 10, 530, 4734, 474986, 5153122, 676701794, 1232820800342, 15623119507746, 34472401720246110, 6163354867874693078, 83483882991733501114, 15658391111267929558466, 42132263940113324754864134

Offset: 3

Author

Henry Bottomley, Oct 02 2003

Keywords

• nonn

Examples

			a(6)=4734 since 13 is the sixth prime and (C(26,13)-2)/13^3 = (10400600-2)/2197 = 4734.
		

Links

• R. R. Aidagulov, 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:1602.02632
• R. P. Stanley, MIT Course OCW 18.S66, The Art of Counting, Spring 2003. (Problem 18)

Crossrefs

Cf. A268512, A268589, A268590.

Programs

Mathematica

Table[(Binomial[2p,p]-2)/p^3,{p,Prime[Range[3,20]]}] (* Harvey P. Dale, Oct 23 2017 *)

Formula

a(n) = A060842(n) / A000040(n).

a(n) = 2 * A034602(n).