A068554 a(n) = n*binomial(2n, n) - 4^n.

-1, -2, -4, -4, 24, 236, 1448, 7640, 37424, 175436, 798984, 3565448, 15672656, 68098936, 293196944, 1253020976, 5322318944, 22491436556, 94632958664, 396682105256, 1657418948624, 6905368852136, 28697991157424, 119000162557136

Offset: 0

Author

N. J. A. Sloane, Mar 23 2002

Keywords

• sign

Comments

Known to be >= 0 for n>3.

References

• Hojoo Lee, Posting to Number Theory List, Feb 18 2002.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000302, A005430.

Programs

Maple

seq(n*binomial(2*n,n)-4^n,n=0..40); # Robert Israel, Nov 13 2016

Mathematica

Table[n*Binomial[2n,n]-4^n,{n,0,30}] (* Harvey P. Dale, Nov 17 2012 *)

Formula

From Robert Israel, Nov 13 2016: (Start)

a(n) = A005430(n) - A000302(n).

G.f.: (2*x-sqrt(1-4*x))/(1-4*x)^(3/2).

a(n) = ((16*(n-2))*(2*n-5)*a(n-3)-(4*(8*n^2-23*n+18))*a(n-2)+(2*(5*n-4))*(n-1)*a(n-1))/(n*(n-1)). (End)