A160637 Hankel transform of A114464(n+1).

1, 1, -2, -8, -32, -128, 1024, 16384, 262144, 4194304, -134217728, -8589934592, -549755813888, -35184372088832, 4503599627370496, 1152921504606846976, 295147905179352825856, 75557863725914323419136, -38685626227668133590597632, -39614081257132168796771975168

Offset: 0

Author

Paul Barry, May 21 2009

Keywords

• easy
• sign

Comments

Hankel transform of A114464(n) is A160636.

This is a generalized Somos-4 sequence. - Michael Somos, Mar 14 2020

Links

• G. C. Greubel, Table of n, a(n) for n = 0..114

Crossrefs

Cf. A011848, A114464, A160636.

Programs

Magma

[(-2)^Floor(Binomial(n+1,2)/2): n in [0..50]]; // G. C. Greubel, May 03 2018

Mathematica

Table[(-2)^Floor[Binomial[n + 1, 2]/2], {n, 0, 50}] (* G. C. Greubel, May 03 2018 *)
a[ n_] := (-2)^Quotient[n (n + 1), 4]; (* Michael Somos, Mar 14 2020 *)

PARI

for(n=0, 50, print1((-2)^floor(binomial(n+1,2)/2), ", ")) \\ G. C. Greubel, May 03 2018

Formula

a(n) = (-2)^floor(C(n+1,2)/2) = (-2)^A011848(n+1).

0 = a(n)*a(n+4) - 2*a(n+1)*a(n+3) + 4*a(n+2)^2 = a(n)*a(n+5) - 4*a(n+1)*a(n+4) for all n in Z. - Michael Somos, Mar 14 2020