A042940 - OEIS

%I #4 Mar 31 2012 13:19:58

%S 1,18,197,1694,12586,84708,530733,3149542,17910398,98409532,525628194,

%T 2741723180,14015785460,70417793992,348499310973,1702076053686,

%U 8216326834550,39251274184780,185770424237398,871859230081092

%N Convolution of Catalan numbers A000108(n+1), n >= 0, with A038846.

%C Also convolution of A018218(n+1), n >= 0, with itself; also convolution of A041001 with A000302 (powers of 4); also convolution of A041005 with A000984 (central binomial coefficients).

%F a(n) = binomial(n+4, 2)*((n+8)*A001700(2)*4^(n+1)-A002457(n+4)/2)/A002457(2), A001700(2)= 10, A002457(2)=30; G.f. (c(x)^2)/(1-4*x)^4, where c(x) = g.f. for Catalan numbers.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_