cp's OEIS Frontend

A184819 E.g.f.: A(x) = Sum_{n>=0} (-log(1-x))^[n*phi^2] / [n*phi^2]!, where [n*phi^2] = A001950(n), the upper Wythoff sequence, and phi = (1+sqrt(5))/2.

%I A184819 #5 Mar 30 2012 18:37:25
%S A184819 1,0,1,3,11,51,289,1940,15056,132579,1305352,14203398,169179053,
%T A184819 2188695718,30552880513,457633893249,7319707872140,124497880667346,
%U A184819 2243512187621332,42695546402663276,855593102807351931
%N A184819 E.g.f.: A(x) = Sum_{n>=0} (-log(1-x))^[n*phi^2] / [n*phi^2]!, where [n*phi^2] = A001950(n), the upper Wythoff sequence, and phi = (1+sqrt(5))/2.
%F A184819 E.g.f.: A(x) = 1/(1-x) - Sum_{n>=1} (-log(1-x))^[n*phi] / [n*phi]!, where [n*phi] = A000201(n), the lower Wythoff sequence.
%F A184819 a(n) = n! - A184818(n) for n>0.
%e A184819 E.g.f.: A(x) = 1 + x^2/2! + 3*x^3/3! + 11*x^4/4! + 51*x^5/5! +...
%e A184819 The series expansion begins:
%e A184819 A(x) = 1 + log(1-x)^2/2! - log(1-x)^5/5! - log(1-x)^7/7! + log(1-x)^10/10! - log(1-x)^13/13! +...+ (-log(1-x))^A001950(n)/A001950(n)! +...
%e A184819 The complementary series begins:
%e A184819 A(x) = 1/(1-x) + log(1-x) + log(1-x)^3/3! - log(1-x)^4/4! - log(1-x)^6/6! - log(1-x)^8/8! + log(1-x)^9/9! +...+ -(-log(1-x))^A000201(n)/A000201(n)! +...
%o A184819 (PARI) {a(n)=local(phi=(sqrt(5)+1)/2,A=1+x+x*O(x^n)); for(i=1, n,A=1+sum(k=1, n,(-log(1-x+x*O(x^n)))^floor(k*phi^2)/floor(k*phi^2)!+x*O(x^n))); n!*polcoeff(A, n)}
%Y A184819 Cf. A184818, A000201, A001950.
%K A184819 nonn
%O A184819 0,4
%A A184819 _Paul D. Hanna_, Jan 22 2011