A118442 Column 0 of triangle A118441, which is the matrix log of triangle A118435.

0, 1, -4, -12, 32, 80, -192, -448, 1024, 2304, -5120, -11264, 24576, 53248, -114688, -245760, 524288, 1114112, -2359296, -4980736, 10485760, 22020096, -46137344, -96468992, 201326592, 419430400, -872415232, -1811939328, 3758096384, 7784628224, -16106127360, -33285996544

Offset: 0

Author

Paul D. Hanna, Apr 28 2006

Keywords

• sign
• easy

Links

• Stefano Spezia, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (0,-8,0,-16).

Crossrefs

Cf. A118441 (triangle), A118443 (row sums); A118435, A001787.

Programs

Mathematica

LinearRecurrence[{0,-8,0,-16},{0,1,-4,-12},40] (* Harvey P. Dale, Dec 29 2014 *)

PARI

{a(n)=polcoeff(x*(1 - 4*x - 4*x^2)/(1 + 4*x^2 +x*O(x^n))^2,n)}

Formula

a(n) = (-1)^floor(n/2)*A001787(n).

G.f.: x*(1 - 4*x - 4*x^2)/(1 + 4*x^2)^2.

E.g.f.: x*(cos(2*x) - sin(2*x)). - Stefano Spezia, Jul 01 2023