%I #8 Mar 24 2017 22:50:21
%S 1,1,-1,3,-11,49,-259,1588,-11080,86589,-747802,7053992,-71912477,
%T 784301582,-9055586513,109372026021,-1360474322540,17016798439534,
%U -204454843326736,2087851221198112,-8301034938962891,-481380640245823637
%N E.g.f.: A(x) = Sum_{n>=0} log(1+x)^[n*phi] / [n*phi]!, where [n*phi] = A000201(n), the lower Wythoff sequence, and phi = (1+sqrt(5))/2.
%D Koh, Youngmee, and Sangwook Ree. "Connected permutation graphs." Discrete Mathematics 307.21 (2007): 2628-2635. See page 2631.
%F E.g.f.: A(x) = 1+x - Sum_{n>=1} log(1+x)^[n*phi^2] / [n*phi^2]!, where [n*phi^2] = A001950(n), the upper Wythoff sequence.
%e E.g.f.: A(x) = 1 + x - x^2/2! + 3*x^3/3! - 11*x^4/4! + 49*x^5/5! +...
%e The series expression begins:
%e A(x) = 1 + 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)! +...
%e The complementary series begins:
%e A(x) = 1+x - 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)! +...
%o (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)/floor(k*phi)!+x*O(x^n))); n!*polcoeff(A, n)}
%Y Cf. A000201, A001950.
%K sign
%O 0,4
%A _Paul D. Hanna_, Jan 22 2011