|
%I #3 Mar 30 2012 18:36:44
%S 0,2,4,8,40,152,1128,6200,61120,442552,5466320,49399320,735847800,
%T 8003532512,139910204080,1784040237288,35858685086352,525504809786112,
%U 11953187179149408,198213959637435608,5037776918810353960
%N Column 1 of triangle A102916.
%C Also equals the interleaving of A102099 with A102922, which equal column 1 of triangle A102098 and its matrix square (A102920), respectively.
%F G.f.: 2 = Sum_{n>=0}(a(2*n+1)+a(2*n+2)*x)*x^(2*n)*Product_{k=2..n+2}(1-k*x) where a(2*n+1)=A102099(n+1) and a(2*n+2)=A102922(n+1) with a(0)=0.
%e 2 = 2*(1-2x) + 4*x*(1-2x) + 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x)
%e + 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x)
%e + 6200*x^6*(1-2x)(1-3x)(1-4x)(1-5x) + 61120*x^7*(1-2x)(1-3x)(1-4x)(1-5x) +...
%e + A102099(n+1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x)
%e + A102922(n+1)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+2)x) + ...
%o (PARI) {a(n)=if(n==0,2,polcoeff(2-sum(k=0,n-1,a(k)*x^k*prod(j=2,k\2+2,1-j*x+x*O(x^n))),n))}
%Y Cf. A102916, A102099, A102922, A102098, A102920.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 21 2005
| 