A112006 A logarithmic transform of the Fibonacci numbers A000045.

0, 1, 2, 7, 32, 194, 1473, 13424, 142722, 1734155, 23704880, 360035434, 6015135425, 109631190368, 2164636394634, 46027826357795, 1048622566013472, 25482771281706578, 657965393430769025, 17988006311731338448

Offset: 0

Author

Wolfdieter Lang, Sep 12 2005

Keywords

• nonn
• easy

Links

• Index entries for sequences related to logarithmic numbers

Crossrefs

Cf. A000045, A007553, A112005.

Formula

E.g.f.: -log(1 - A(x)) with the e.g.f. A(x):=exp(x/2)*sinh(sqrt(5)*x/2)/(sqrt(5)/2) of A000045.

a(n) = Fibonacci(n) + Sum_{k=1..n-1} binomial(n-1,k-1) * a(k) * Fibonacci(n-k). - Ilya Gutkovskiy, Jul 11 2020