A180869 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.

1, 1, -1, 3, -11, 49, -259, 1588, -11080, 86589, -747802, 7053992, -71912477, 784301582, -9055586513, 109372026021, -1360474322540, 17016798439534, -204454843326736, 2087851221198112, -8301034938962891, -481380640245823637

Offset

0,4

References

Koh, Youngmee, and Sangwook Ree. "Connected permutation graphs." Discrete Mathematics 307.21 (2007): 2628-2635. See page 2631.

Links

Table of n, a(n) for n=0..21.

Formula

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.

Example

E.g.f.: A(x) = 1 + x - x^2/2! + 3*x^3/3! - 11*x^4/4! + 49*x^5/5! +...
The series expression begins:
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)! +...
The complementary series begins:
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)! +...

Prog

(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)}

Crossrefs

Cf. A000201, A001950.

Sequence in context: A326521 A340813 A004211 * A357836 A356291 A001339

Adjacent sequences: A180866 A180867 A180868 * A180870 A180871 A180872

Keyword

sign

Author

Paul D. Hanna, Jan 22 2011

Status

approved