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A111585
G.f.: A(x) = ( G(x)^11 - G(x^11) - 11*x*((1-x^10)/(1-x))/(1-x^11) )/(121*x^2) where G(x) is the g.f. of A110644.
A110644 is formed by selecting every 11-th term of A084066; surprisingly, the self-convolution 11-th power of A110644 is congruent modulo 121 to A084066, which consists entirely of numbers 1 through 11.