A051745 a(n) = n*(n^4 + 10*n^3 + 35*n^2 + 50*n + 144)/120.

2, 8, 24, 60, 131, 258, 469, 800, 1296, 2012, 3014, 4380, 6201, 8582, 11643, 15520, 20366, 26352, 33668, 42524, 53151, 65802, 80753, 98304, 118780, 142532, 169938, 201404, 237365, 278286, 324663, 377024, 435930, 501976, 575792, 658044, 749435, 850706, 962637

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999

Keywords

• easy
• nonn

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Magma

[n*(n^4 + 10*n^3 + 35*n^2 + 50*n + 144)/120: n in [1..30]]; // G. C. Greubel, Nov 25 2017

Mathematica

Table[Binomial[n+4,n-1]+Binomial[n,n-1],{n,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{2,8,24,60,131,258},40] (* Harvey P. Dale, Apr 07 2013 *)

PARI

Vec(x*(x^4-4*x^3+6*x^2-4*x+2)/(x-1)^6 + O(x^100)) \\ Colin Barker, Mar 19 2015

Formula

a(n) = binomial(n+4, n-1) + binomial(n, n-1).

a(n) = C(n+4, 5) + n = A000389(n+4) + n.

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), with a(1)=2, a(2)=8, a(3)=24, a(4)=60, a(5)=131, a(6)=258. - Harvey P. Dale, Apr 07 2013

G.f.: x*(x^4-4*x^3+6*x^2-4*x+2) / (x-1)^6. - Colin Barker, Mar 19 2015

E.g.f.: x*(240 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x)/120. - G. C. Greubel, Nov 25 2017