A354018 Expansion of e.g.f. -log(1-x)/(1 + log(1-x) - log(1-x)^2)

0, 1, 3, 20, 172, 1864, 24248, 368136, 6388128, 124711944, 2705241672, 64550432352, 1680280323984, 47383464508080, 1438986494794704, 46821994627363968, 1625069178022566528, 59927028756823323648, 2339899614887520358656, 96439023491479275172608

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} k! * Fibonacci(k) * |Stirling1(n,k)|.

a(n) ~ n! * (sqrt(5) - 1) / (2 * sqrt(5) * exp((sqrt(5) - 1)/2) * (1 - exp((1 - sqrt(5))/2))^(n+1)). - Vaclav Kotesovec, May 15 2022

Mathematica

Table[Sum[k! * Fibonacci[k] * Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 15 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-x)/(1+log(1-x)-log(1-x)^2))))
(PARI) a(n) = sum(k=0, n, k!*fibonacci(k)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A000045, A005444, A005445, A265165, A320352, A354013.

Sequence in context: A213377 A357094 A216583 * A154644 A321276 A000891

Adjacent sequences: A354015 A354016 A354017 * A354019 A354020 A354021

Keyword

nonn

Author

Seiichi Manyama, May 14 2022

Status

approved