A127881 Integers of the form x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1 with x > 0.

241231, 7057861, 21166951, 52066891, 216295321, 654480151, 1619368381, 2411089396, 3486017011, 6776093041, 12182173471, 20592045301, 26260194241, 33113005531, 51096161161, 76160729191, 110218336621, 131302849486

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn

Comments

Generating polynomial is Schur's polynomial of 5-degree. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisible by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A127873, A127874, A127875, A127876, A127877, A127878, A127879, A127880, A127882, A127883, A127884.

Programs

Mathematica

a = {}; Do[If[IntegerQ[1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120], AppendTo[a, 1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120]], {x, 1, 1000}]; a
Select[Table[ x^5/120+x^4/24+x^3/6+x^2/2+x+1,{x,450}],IntegerQ] (* Harvey P. Dale, Jan 20 2019 *)

PARI

for(x=1,500,y=x^5+5*x^4+20*x^3+60*x^2+120*x+120;if(y%120==0,print1(y/120, ", "))) \\ Michael B. Porter, Jan 29 2010

PARI

isA127881(n)={local(r);r=0;fordiv(120*n-120,x,if(x^5/120+x^4/24+x^3/6+x^2/2+x+1==n,r=1));r} \\ Michael B. Porter, Jan 29 2010