A139174 a(n) = (n!-4)/4.

5, 29, 179, 1259, 10079, 90719, 907199, 9979199, 119750399, 1556755199, 21794572799, 326918591999, 5230697471999, 88921857023999, 1600593426431999, 30411275102207999, 608225502044159999

Offset: 4

Author

Artur Jasinski, Apr 11 2008

Keywords

• nonn
• easy

Comments

In the solution set of the equation, n! + s^2 = m^2, for any n>=4 the maximum value of s is (n!-4)/4. - Sudipta Mallick, Jul 27 2019

Links

• Sudipta Mallick, Table of n, a(n) for n = 4..400 (terms 4..300 from Vincenzo Librandi)

Crossrefs

Cf. A033312, A139172, A139173, A139174, A139175, A139176, A139177, A139183, A139184.

Programs

Magma

[(Factorial(n)-4)/4: n in [4..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica

Table[(n! - 4)/4, {n, 4, 20}]

Formula

a(n) = numerator(((n+2)!-4)/(7*(n+2)!)), with offset 2. [Gary Detlefs, Nov 07 2010]

E.g.f.: -exp(x)-(12+x^2*(-6+(-4+x)*x))/(12*(-1+x)). - Stefano Spezia, Sep 08 2019

Extensions

Definition corrected by Gary Detlefs, Nov 07 2010