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A367787
Let b(0) = 1, b(n) = Sum_{k=0..n-1} b(k) / b(n-k-1), then a(n) is the numerator of b(n).
1
1, 1, 2, 7, 44, 3459, 21398845, 204701870532176, 47683439994850565666251869149, 203292005443961363023193564438853229653319486912062841397
OFFSET
0,3
COMMENTS
The next term is too large to include.
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_] := Numerator[b[n]]; Table[a[n], {n, 0, 9}]
CROSSREFS
Cf. A000108, A022857, A022858, A073833, A367788 (denominators).
Sequence in context: A006118 A083670 A270357 * A108240 A064606 A331711
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, Nov 30 2023
STATUS
approved