A115129 Partial sums of A005587. Fourth column of triangle A115127.

14, 56, 146, 311, 586, 1015, 1652, 2562, 3822, 5522, 7766, 10673, 14378, 19033, 24808, 31892, 40494, 50844, 63194, 77819, 95018, 115115, 138460, 165430, 196430, 231894, 272286, 318101, 369866, 428141, 493520, 566632, 648142, 738752, 839202

Offset: 0

Author

Wolfdieter Lang, Jan 13 2006

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A024191 (third column of A115127).

Programs

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{14,56,146,311,586,1015},40] (* or *) CoefficientList[Series[(14-28x+20x^2-5x^3)/(1-x)^6,{x,0,40}],x] (* Harvey P. Dale, Apr 24 2016 *)

Formula

G.f.: (14 - 28*x + 20*x^2 - 5*x^3)/(1 - x)^6.

a(n)=A115127(n+4, 4), n>=1.

a(0)=14, a(1)=56, a(2)=146, a(3)=311, a(4)=586, a(5)=1015, 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). - Harvey P. Dale, Apr 24 2016