A188897 a(n) = lcm(n, n+1, n+2, n+3, n+4, n+5, n+6, n+7)/840.

0, 1, 3, 3, 33, 33, 429, 429, 429, 858, 4862, 14586, 25194, 25194, 1938, 21318, 490314, 245157, 72105, 312455, 148005, 148005, 4292145, 390195, 525915, 2103660, 4628052, 6052068, 672452, 2017356, 2573868

Offset: 0

Author

Gary Detlefs, Apr 19 2011

Keywords

• nonn

Crossrefs

Cf. A189144.

Programs

Maple

seq(lcm(n,n+1,n+2,n+3,n+4,n+5,n+6,n+7)/840, n=0..30);
p:=n-> 8*3^((n-1)^2 mod 3):q:=n-> 4*(((n-2)^4 mod 5 +(n-1)^4)mod5)-3:f:=n-> 1-(n^6 mod 7): seq((n+7)!/(5040*(n-1)!*p(n)*q(n)*(1+6*f(n))),n=1..30)

Formula

a(n) = (n+7)!/(5040*(n-1)!*p(n)*q(n)*(1+6*f(n))), n > 1 where

p(n) = 8*3^((n-1)^2 mod 3),

q(n) = 4*(((n-2)^4 mod 5 +(n-1)^4) mod 5)-3, and

f(n) = 1-(n^6 mod 7).

Extensions

Missing term a(5)=33 inserted by Georg Fischer, Mar 31 2025