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%I #3 Jun 16 2016 23:27:39
%S 3,15,35,315,693,1001,6435,109395,230945,969969,2028117,16900975,
%T 35102025,145422675,20036013,9917826435,20419054425,27981667175,
%U 172308161025,282585384081,964378691705,11835556670925,24185702762325
%N Numerators of the column sums of the EG1 matrix coefficients
%C For the definition of the EG1 matrix coefficients see A162440.
%C We define the columns sums by cs(n) = sum(EG1[2*m-1,n], m = 1.. infinity) for n => 2.
%C The row sums of the EG1 matrix follow the same pattern as those of its even counterpart the EG2 matrix, see A161739 and the formulas.
%F a(n) = numer(cs(n)) and denom(cs(n)) = A162442(n) with cs(n) = (2^(2-2*n)/(n-1))*((2*n-1)!/((n-1)!^2)).
%F cs(n) = 2*EG1[ -1,n]/(n-1) with EG1[ -1,n] = 2^(1-2*n)*(2*n-1)!/((n-1)!^2).
%F cs(n) = (1/(n-1))*A001803(n-1)/A046161(n-1) for n=>2.
%F rs(2*m-1,p=0) = sum((n^p)*EG1(2*m-1,n), n = 1..infinity) = 2*zeta(2*m-2) for m =>2.
%Y Equals (2*n-1)*A052468(n-1)
%Y Cf. A162440 and A162442 [denom(cs(n))].
%Y Cf. A161739 (RSEG2 triangle), A001803 and A046161.
%K easy,frac,nonn
%O 2,1
%A _Johannes W. Meijer_, Jul 06 2009
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