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
Programs
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Mathematica
a[ n_] := 2^Quotient[(n+1)^2, 3]; (* Michael Somos, May 12 2022 *)
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PARI
{a(n) = 2^((n+1)^2\3)}; /* Michael Somos, May 12 2022 */
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
Comments