A181888 Second column of triangle in A182971.

0, 0, 9, 64, 259, 784, 1974, 4368, 8778, 16368, 28743, 48048, 77077, 119392, 179452, 262752, 375972, 527136, 725781, 983136, 1312311, 1728496, 2249170, 2894320, 3686670, 4651920, 5818995, 7220304, 8892009, 10874304, 13211704, 15953344, 19153288, 22870848, 27170913, 32124288, 37808043, 44305872, 51708462, 60113872

Offset: 1

Author

N. J. A. Sloane, Feb 01 2011

Keywords

• nonn

Comments

These are scaled central factorial numbers (see A182971).

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Cf. A182971. Bisections give A001823 and A181889.

Programs

Mathematica

CoefficientList[Series[x^3(9+x)/(1-x)^7,{x,0,40}],x] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{0,0,0,9,64,259,784},50] (* Harvey P. Dale, Jul 03 2013 *)

Formula

G.f.: x^3*(9+x)/(1-x)^7.

a(1)=0, a(2)=0, a(3)=0, a(4)=9, a(5)=64, a(6)=259, a(7)=784, 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, Jul 03 2013