A134751 Hankel transform of expansion of (1/(1-x^2))c(x/(1-x^2)), where c(x) is the g.f. of A000108.

1, 2, 8, 32, 256, 4096, 65536, 2097152, 134217728, 8589934592, 1099511627776, 281474976710656, 72057594037927936, 36893488147419103232, 37778931862957161709568, 38685626227668133590597632

Offset

0,2

Comments

Hankel transform of A105864.

The sequence 1,1,2,8,... with general term 2^floor(n^2/3) is the Hankel transform of A109033. - Paul Barry, Dec 14 2008

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = 2^floor((n+1)^2/3);

a(n) = Product_{k=1..n} (5/3 - 2*cos(2*Pi*k/3)/3)^(n-k+1);

a(n) = Product_{k=1..n} A130196(k)^(n-k+1).

a(n) = 4*a(n-1)*a(n-3)/a(n-4). Somos-4 sequence associated to, e.g., y^2 = 1 - 8x + 16x^2 - 8x^3. - Paul Barry, Nov 27 2009

a(n) = a(-2-n) for all n in Z. - Michael Somos, May 12 2022

Mathematica

a[ n_] := 2^Quotient[(n+1)^2, 3]; (* Michael Somos, May 12 2022 *)

Prog

(PARI) {a(n) = 2^((n+1)^2\3)}; /* Michael Somos, May 12 2022 */

Crossrefs

Sequence in context: A262480 A062797 A369645 * A139014 A063505 A085466

Adjacent sequences: A134748 A134749 A134750 * A134752 A134753 A134754

Keyword

easy,nonn

Author

Paul Barry, Nov 08 2007

Status

approved