A348875 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(2*x)).

1, 2, 8, 56, 656, 13184, 477248, 32524928, 4295916032, 1117098857984, 576442191401984, 592587279827787776, 1215991461595100598272, 4985567391504232291377152, 40861715233637664786276712448, 669641809249948891254213657460736, 21945501536426419427607885034600595456

Offset: 0

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

• nonn

Crossrefs

Cf. A006318, A015083, A348876, A348877.

Programs

Mathematica

nmax = 16; A[] = 0; Do[A[x] = 1/(1 - x - x A[2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[2^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1).

a(n) ~ c * 2^(n*(n-1)/2), where c = 1/(A048651 * A083864) = 2*Product_{j>=1} (2^j+1)/(2^j-1) = 16.51197587155650013108828169886454625305400323357646... - Vaclav Kotesovec, Nov 03 2021