|
%I #18 May 15 2022 04:22:23
%S 0,1,3,20,172,1864,24248,368136,6388128,124711944,2705241672,
%T 64550432352,1680280323984,47383464508080,1438986494794704,
%U 46821994627363968,1625069178022566528,59927028756823323648,2339899614887520358656,96439023491479275172608
%N Expansion of e.g.f. -log(1-x)/(1 + log(1-x) - log(1-x)^2)
%F a(n) = Sum_{k=0..n} k! * Fibonacci(k) * |Stirling1(n,k)|.
%F 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
%t Table[Sum[k! * Fibonacci[k] * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, May 15 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-x)/(1+log(1-x)-log(1-x)^2))))
%o (PARI) a(n) = sum(k=0, n, k!*fibonacci(k)*abs(stirling(n, k, 1)));
%Y Cf. A000045, A005444, A005445, A265165, A320352, A354013.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 14 2022
|
