Search: id:A094639
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%I A094639
%S A094639 1,2,6,31,227,1991,19415,203456,2248356,25887400,307993016,3763786812,
%T A094639 47032778956,598933188956,7751562502556,101741582076581,
%U A094639 1351906409905481,18159677984049581,246298405721739581
%N A094639 Partial sums of squares of Catalan numbers (A000108).
%H A094639 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A094639 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%F A094639 a(n) = Sum[ ((2k)!/(k!)^2/(k+1))^2, {k,0,n}. - Alexander Adamchuk, Feb 
               16 2008
%F A094639 Sum_{i=1..n} [c(i)]^2 = Sum_{i=1..n} [C(2*i-2, i-1)/i]^2 = (1/(n-1)!)^2 
               * [ n^C(2*n-4, 1) + {2*C(n-1, 2)}*n^(2*n-5) + {C(n-2, 0) + 4*C(n-2, 
               1) + 13*C(n-2, 2) + 22*C(n-2, 3) + 12*C(n-2, 4)}*n^C(2*n-6, 1) + 
               {12*C(n-3, 1) + 152*C(n-3, 2) + 458*C(n-3, 3) + 640*C(n-3, 4) + 440*C(n-3, 
               5) + 120*C(n-3, 6)}*n^(2*n-7) + {40*C(n-4, 0) + 313*C(n-4, 1) + 2332*C(n-4, 
               2) + 9536*C(n-4, 3) + 21409*C(n-4, 4) + 28068*C(n-4, 5) + 21700*C(n-4, 
               6) + 9240*C(n-4, 7) + 1680*C(n-4, 8) + ... + C(n-3, 0)*((n-1)!)^2 
               ].
%Y A094639 Cf. A000108, A094638, A014137, A001246, A033536, A000984, A006134, A082894, 
               A002897, A079727.
%Y A094639 Sequence in context: A058028 A054141 A007710 this_sequence A113719 A018225 
               A075845
%Y A094639 Adjacent sequences: A094636 A094637 A094638 this_sequence A094640 A094641 
               A094642
%K A094639 easy,nonn
%O A094639 0,2
%A A094639 Andre F. Labossiere (boronali(AT)laposte.net), May 27 2004

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