A367788 Let b(0) = 1, b(n) = Sum_{k=0..n-1} b(k) / b(n-k-1), then a(n) is the denominator of b(n).

1, 1, 1, 2, 7, 308, 1065372, 5699432573835, 742435596532024691458409520, 1770094160863794205114840009375146894748207874734794924

Offset

0,4

Comments

The next term is too large to include.

Links

Table of n, a(n) for n=0..9.

Formula

G.f. for fractions satisfies: 1 / Sum_{n>=0} b(n) * x^n = 1 - x * Sum_{n>=0} x^n / b(n).

Example

1, 1, 2, 7/2, 44/7, 3459/308, 21398845/1065372, 204701870532176/5699432573835, ...

Mathematica

b[0] = 1; b[n_] := b[n] = Sum[b[k]/b[n - k - 1], {k, 0, n - 1}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 9}]

Crossrefs

Cf. A000108, A022857, A022858, A073834, A367787 (numerators).

Sequence in context: A187603 A290637 A260967 * A128456 A137666 A137665

Adjacent sequences: A367785 A367786 A367787 * A367789 A367790 A367791

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Nov 30 2023

Status

approved