A119330 Expansion of (1-x)^2/((1-x)^4-2x^4).

1, 2, 3, 4, 7, 18, 49, 120, 265, 554, 1155, 2476, 5455, 12138, 26881, 58992, 128689, 280466, 612579, 1341268, 2940151, 6443778, 14111857, 30886632, 67590649, 147934010, 323850531, 709047292, 1552412671, 3398703066, 7440375937

Offset: 0

Author

Paul Barry, May 14 2006

Keywords

• easy
• nonn

Comments

Row sums of A119329. Binomial transform of A119332, or (1,1,0,0,2,2,0,0,4,4,...).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,1).

Programs

Mathematica

CoefficientList[Series[(1-x)^2/((1-x)^4-2x^4),{x,0,50}],x] (* or *) LinearRecurrence[{4,-6,4,1},{1,2,3,4},50] (* Harvey P. Dale, Jul 20 2021 *)

Formula

a(n)=4a(n-1)-6a(n-2)+4a(n-3)+a(n-4); a(n)=sum{k=0..n, sum{j=0..n-k, C(k,2j)C(n-k,2j)*2^j}}.