%I A102223
%S A102223 0,1,3,22,323,7906,290262,14919430,1022475715,90094491994,9923239949978,
%T A102223 1335853771297750,215797095378591542,41198645313603207990,
%U A102223 9176288655853717238830,2358300288047799986966722
%N A102223 Column 0 of triangular matrix A102222, which equals -log[2*I - A008459].
%C A102223 Triangle A008459 consists of squared binomial coefficients.
%F A102223 a(n) = 1 + (1/n)*Sum_{k=0..n-1} C(n, k)^2*k*a(k) for n>0, with a(0)=0.
%F A102223 Sum_{n>=0} a(n)*x^n/n!^2 = -ln(2-BesselI(0,2*sqrt(x))). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jul 16 2006
%e A102223 a(2) = 3 = 1 + (1*0*0 + 4*1*1)/2,
%e A102223 a(3) = 22 = 1 + (1*0*0 + 9*1*1 + 9*2*3)/3,
%e A102223 a(4) = 323 = 1 + (1*0*0 + 16*1*1 + 36*2*3 + 16*3*22)/4,
%e A102223 a(5) = 7906 = 1 + (1*0*0 + 25*1*1 + 100*2*3 + 100*3*22 + 25*4*323)/5.
%o A102223 (PARI) a(n)=if(n<1,0,1+sum(k=0,n-1,binomial(n,k)^2*k*a(k))/n)
%Y A102223 Cf. A008459, A102220, A102222.
%Y A102223 Sequence in context: A144681 A124567 A161967 this_sequence A046947 A002485 
               A099750
%Y A102223 Adjacent sequences: A102220 A102221 A102222 this_sequence A102224 A102225 
               A102226
%K A102223 nonn
%O A102223 0,3
%A A102223 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2004