A118792 E.g.f.: -log(1 - (1 - sqrt(5 - 4*exp(x)) )/2 ).

0, 1, 4, 30, 352, 5670, 116344, 2902830, 85326112, 2887962870, 110620824904, 4730842053630, 223445584599472, 11552029520192070, 648869447924011864, 39347855472366932430, 2562065820090343738432, 178286102174571726213270

Offset

0,3

Comments

Also equals the unsigned row sums of triangle A118791 (offset without leading zero).

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (n-1)!*Sum_{k=0..n-1} abs( [x^k] (x/log(1-x-x^2))^n ) for n>0.

a(n) ~ sqrt(5/2)*n^(n-1)/(exp(n)*(log(5/4))^(n-1/2)). - Vaclav Kotesovec, Jun 26 2013

Example

E.g.f.: A(x) = x + 2*x^2 + 30/6*x^3 + 352/24*x^4 + 5670/120*x^5 +...

Mathematica

CoefficientList[Series[-Log[1-(1-Sqrt[5-4*Exp[x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

Prog

(PARI) a(n)=local(x=X+X^2*O(X^n)); n!*polcoeff(-log(1-(1-sqrt(5-4*exp(x)))/2), n, X)
(PARI) /* As the unsigned row sums of A118791: */ a(n)=local(x=X+X^2*O(X^n)); if(n<1, 0, (n-1)!*sum(k=0, n-1, abs(polcoeff(((-x/log(1-x-x^2)))^n, k, X))))

Crossrefs

Cf. A118791.

Sequence in context: A089918 A132622 A218296 * A317030 A192549 A303001

Adjacent sequences: A118789 A118790 A118791 * A118793 A118794 A118795

Keyword

nonn

Author

Paul D. Hanna, Apr 30 2006

Status

approved