A398040 - OEIS

%I #8 Jul 18 2026 08:42:47

%S 1,4,20,80,340,1360,5520,22080,88660,354640,1419920,5679680,22724240,

%T 90896960,363609920,1454439680,5817847380,23271389520,93085912720,

%U 372343650880,1489376023440,5957504093760,23830022054720,95320088218880,381280375599760,1525121502399040

%N G.f. A(x) satisfies A(x) = A(x^2) / (1-4*x), with A(0) = 1.

%F G.f.: Product_{k>=0} 1/(1 - 4*x^(2^k)).

%F G.f.: 1 + 4 * Sum_{j>=0} x^(2^j) / Product_{k=0..j} (1 - 4*x^(2^k)).

%F a(0) = 1; for n >= 1, a(n) = 4*a(n-1) + a(n/2) if 2|n, and a(n) = 4*a(n-1) otherwise.

%F a(n) = Sum_{k=0..floor(n/2)} 4^(n-2*k) * a(k) for n >= 1.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, logint(N, 2), 1-4*x^2^k))

%Y Cf. A018819, A309728, A398039.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Jul 18 2026