0,3

Limit a(n)/2^[n*(n-1)/2] = 1.97254925752982255...

G.f.: A(x) = 1 + x*B(x)^2; B(x) = 1 + x*C(x)^4; C(x) = 1 + x*D(x)^8;

D(x) = 1 + x*E(x)^16; E(x) = 1 + x*F(x)^32; ...

where the respective sequences begin:

B=[1,1,4,38,724,26385,1837224,247455640,65256486712,...];

C=[1,1,8,156,6008,436870,60346328,16118073852,8445009616488,...];

D=[1,1,16,632,48944,7110684,1956587408,1040720206536,...];

E=[1,1,32,2544,395104,114749560,63023951008,66902165283280,...];

F=[1,1,64,10208,3175104,1843872240,2023417888576,...].

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(2^(n-j))); polcoeff(A, n)}

Cf. A095793 (variant).

Adjacent sequences: A120956 A120957 A120958 this_sequence A120960 A120961 A120962

Sequence in context: A113146 A069234 A086929 this_sequence A125797 A106163 A068595

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jul 28 2006