A099531 Expansion of (1+x)^3/((1+x)^3+x^4).

1, 0, 0, 0, -1, 3, -6, 10, -14, 15, -7, -20, 80, -188, 351, -549, 702, -622, -42, 1839, -5471, 11560, -20064, 29144, -33329, 21059, 27730, -142182, 355626, -689121, 1114937, -1490892, 1461360, -337220, -2996465, 10030587, -22226506, 39921442, -60118930, 72788383, -55703295, -31057776

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• sign

Comments

Binomial transform is A099530.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1,-1).

Crossrefs

Cf. A099529.

Programs

Mathematica

CoefficientList[Series[(1+x)^3/((1+x)^3+x^4),{x,0,50}],x] (* or *) LinearRecurrence[{-3,-3,-1,-1},{1,0,0,0},50] (* Harvey P. Dale, Feb 21 2016 *)

Formula

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