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a(n)=Sum(i+j+k+l+...+r+s=n) A005316(i)*A005316(j)*...*A005316(s) and the ordered partition of n runs over all odd i, all even j,k,.., r, all i,j,...,r,s>=1.
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%I #7 Jul 29 2013 08:36:01

%S 1,1,2,3,8,14,42,79,254,506,1702,3548,12320,26666,94794,211751,766362,

%T 1758352,6453812,15150922,56238710,134659120

%N a(n)=Sum(i+j+k+l+...+r+s=n) A005316(i)*A005316(j)*...*A005316(s) and the ordered partition of n runs over all odd i, all even j,k,.., r, all i,j,...,r,s>=1.

%C A lower bound to A076876. a(n) counts the cases where all crossings k are East of the crossings i, all crossings l East of the crossings j etc. Some backwinding interlaced crossings are counted in A076876(n) but not here.

%K nonn,more

%O 0,3

%A _R. J. Mathar_, May 06 2006