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 A102223 Column 0 of triangular matrix A102222, which equals -log[2*I - A008459]. 8

%I

%S 0,1,3,22,323,7906,290262,14919430,1022475715,90094491994,

%T 9923239949978,1335853771297750,215797095378591542,

%U 41198645313603207990,9176288655853717238830,2358300288047799986966722

%N Column 0 of triangular matrix A102222, which equals -log[2*I - A008459].

%C Triangle A008459 consists of squared binomial coefficients.

%F 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 Sum_{n>=0} a(n)*x^n/n!^2 = -log(2-BesselI(0,2*sqrt(x))). - _Vladeta Jovovic_, Jul 16 2006

%e a(2) = 3 = 1 + (1*0*0 + 4*1*1)/2,

%e a(3) = 22 = 1 + (1*0*0 + 9*1*1 + 9*2*3)/3,

%e a(4) = 323 = 1 + (1*0*0 + 16*1*1 + 36*2*3 + 16*3*22)/4,

%e a(5) = 7906 = 1 + (1*0*0 + 25*1*1 + 100*2*3 + 100*3*22 + 25*4*323)/5.

%o (PARI) a(n)=if(n<1,0,1+sum(k=0,n-1,binomial(n,k)^2*k*a(k))/n)

%Y Cf. A008459, A102220, A102222.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 31 2004

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)