A060103 Fourth column (m=3) of triangle A060102.

1, 13, 71, 259, 742, 1806, 3906, 7722, 14223, 24739, 41041, 65429, 100828, 150892, 220116, 313956, 438957, 602889, 814891, 1085623, 1427426, 1854490, 2383030, 3031470, 3820635, 4773951, 5917653

Offset: 0

Author

Wolfdieter Lang, Apr 06 2001

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 (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Cf. A000012, A000290, A002417, A060102.

Programs

Mathematica

Table[((4n^2+20n+15)Binomial[n+4,4])/15,{n,0,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{1,13,71,259,742,1806,3906},30] (* Harvey P. Dale, Dec 16 2012 *)

Formula

a(n) = (4*n^2+20*n+15)*binomial(n+4, 4)/15.

G.f.: (1+6*x+x^2)/(1-x)^7.

a(0)=1, a(1)=13, a(2)=71, a(3)=259, a(4)=742, a(5)=1806, a(6)=3906, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Dec 16 2012