A127883 a(n) = 60*(n^5/120 + n^4/24 + n^3/6 + n^2/2 + n + 1).

163, 436, 1104, 2572, 5485, 10788, 19786, 34204, 56247, 88660, 134788, 198636, 284929, 399172, 547710, 737788, 977611, 1276404, 1644472, 2093260, 2635413, 3284836, 4056754, 4967772, 6035935, 7280788, 8723436, 10386604, 12294697

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn
• easy

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

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A127873-A127882.

Programs

Magma

[n^4*(n+5)/2+10*(n^3+3*n^2+6*n+6): n in [1..30]]; // Bruno Berselli, Apr 03 2012

Maple

A127883:=n->60*(n^5/120 + n^4/24 + n^3/6 + n^2/2 + n + 1); seq(A127883(n), n=1..40); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

Table[1/2 (120+x (120+x (60+x (20+x (5+x))))), {x,40}] (* Harvey P. Dale, Mar 12 2011 *)
CoefficientList[Series[(163 - 542 x + 933 x^2 - 772 x^3 + 338 x^4 - 60 x^5)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 28 2014 *)

Formula

G.f.: x*(163-542*x+933*x^2-772*x^3+338*x^4-60*x^5)/(1-x)^6. - Colin Barker, Apr 02 2012