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%I #4 Mar 31 2012 13:19:58
%S 1,14,125,906,5810,34364,191901,1026610,5312230,26767940,131990066,
%T 639210404,3048892740,14354652152,66828135005,308078809794,
%U 1408022619806,6385966846580,28765327498278,128777533131500
%N Convolution of A000108(n+1), n >= 0, (Catalan numbers) with A038845 (3-fold convolution of powers of 4).
%C Also convolution of A038836 with A000984 (central binomial coefficients); also convolution of A001791(n+1), n >= 0, with A002802; also convolution of A008549(n+1), n >= 0, with A002697; also convolution of A029760 with A002457; also convolution of A038806(n+1), n >= 0, with A000302 (powers of 4).
%F a(n) = (n+3)*(3*(n+6)*2^(2*n+3)-(n+4)*binomial(2*n+7, n+3))/12; G.f. (c(x)^2)/(1-4*x)^3, where c(x) = g.f. for Catalan numbers.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_