A261886 - OEIS

%I #5 Sep 04 2015 20:16:44

%S 0,1,-2,11,-96,1080,-13776,179592,-2257536,36167616,-1328400000,

%T 53474351040,-364978483200,-111366266618880,2057176091013120,

%U 861071536310630400,-50092279632602726400,-9303569614922165452800,1142810852264472571084800,154051064897857365779251200,-35956459453770594679062528000

%N E.g.f. satisfies: A(x) = A( x/(1-x)^3 ) * (1-x)/(1+2*x) with A(0)=0.

%C a(n) = A261885(n)/3.

%H Paul D. Hanna, <a href="/A261886/b261886.txt">Table of n, a(n) for n = 0..200</a>

%e E.g.f.: A(x) = x - 2*x^2/2! + 11*x^3/3! - 96*x^4/4! + 1080*x^5/5! - 13776*x^6/6! + 179592*x^7/7! - 2257536*x^8/8! + 36167616*x^9/9! - 1328400000*x^10/10! +...

%e A(x/(1-x)^3) = x + 4*x^2/2! + 11*x^3/3! + 36*x^4/4! + 300*x^5/5! + 984*x^6/6! - 6384*x^7/7! + 564864*x^8/8! + 615744*x^9/9! - 598890240*x^10/10! +...

%e where A(x/(1-x)^3) = (1+2*x)/(1-x)*A(x).

%o (PARI) /* E.g.f. satisfies: A(x) = (1-x)/(1+2*x)*A(x/(1-x)^3): */

%o {a(n)=local(A=x, B); for(m=2, n, B=(1-x)/(1+2*x+O(x^(n+3)))*subst(A, x, x/(1-x+O(x^(n+3)))^3); A=A-polcoeff(B, m+1)*x^m/(m-1)/3); n!*polcoeff(A, n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A261885.

%K sign

%O 0,3

%A _Paul D. Hanna_, Sep 04 2015