A127276 Hankel transform of A127275.

1, 1, -2, -16, -64, -208, -608, -1664, -4352, -11008, -27136, -65536, -155648, -364544, -843776, -1933312, -4390912, -9895936, -22151168, -49283072, -109051904, -240123904, -526385152, -1149239296, -2499805184, -5419040768

Offset: 0

Author

Paul Barry, Jan 10 2007

Keywords

• sign

Comments

The inverse binomial transform of this sequence yields 1, 0, -3, -8,..., which is 1 followed by the negated terms of A005563. [Paul Curtz, Dec 07 2010]

The smallest odd prime divisor of a(n) is >= 13. - Vladimir Shevelev, Feb 03 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A076616, A176126, A236999.

Programs

Magma

[2^n-n*(n+1)*2^(n-2): n in [0..30]]; // Vincenzo Librandi, Aug 11 2011

Maple

A127276:=n->2^n - n*(n + 1)*2^(n - 2); seq(A127276(n), n=0..26); # Wesley Ivan Hurt, Dec 02 2013

Mathematica

Table[2^n - n*(n + 1)*2^(n - 2), {n, 0, 26}] (* Wesley Ivan Hurt, Dec 02 2013 *)

Formula

Conjecture: G.f.: -(4*x-1)*(x-1) / ( (2*x-1)^3 ) and a(n) = 2^n-n*(n+1)*2^(n-2). - R. J. Mathar, Dec 11 2010

a(n) = A178987(n) - A178987(n+1). - Klaus Brockhaus, Jan 08 2011