A348860 G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(2*x))).

1, 0, 1, 4, 37, 632, 20905, 1359692, 175426573, 45086173824, 23129393794129, 23707675064224020, 48577049664823958389, 199020196349510773741576, 1630572517436087330046884473, 26716930897552073378560239594588, 875487110213852689248519499248558685

Offset

0,4

Links

Table of n, a(n) for n=0..16.

Formula

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

a(n) ~ c * 2^(n*(n-1)/2), where c = 0.658663398267275680037834076118178644268023291808559507713140088111498143... - Vaclav Kotesovec, Nov 02 2021

Mathematica

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

Crossrefs

Cf. A005043, A015083, A348861, A348862.

Sequence in context: A177385 A155926 A094408 * A352469 A061683 A084283

Adjacent sequences: A348857 A348858 A348859 * A348861 A348862 A348863

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2021

Status

approved