A161739 -id:A161739 - cp's OEIS frontend

A162441 Numerators of the column sums of the EG1 matrix coefficients.

3, 15, 35, 315, 693, 1001, 6435, 109395, 230945, 969969, 2028117, 16900975, 35102025, 145422675, 20036013, 9917826435, 20419054425, 27981667175, 172308161025, 282585384081, 964378691705, 11835556670925, 24185702762325

Offset: 2

Johannes W. Meijer, Jul 06 2009

For the definition of the EG1 matrix coefficients see A162440.
We define the columns sums by cs(n) = sum(EG1[2*m-1,n], m = 1.. infinity) for n => 2.
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.

Equals (2*n-1)*A052468(n-1)
Cf. A162440 and A162442 [denom(cs(n))].
Cf. A161739 (RSEG2 triangle), A001803 and A046161.

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)).
cs(n) = 2*EG1[ -1,n]/(n-1) with EG1[ -1,n] = 2^(1-2*n)*(2*n-1)!/((n-1)!^2).
cs(n) = (1/(n-1))*A001803(n-1)/A046161(n-1) for n=>2.
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.

cp's OEIS Frontend

A162441 Numerators of the column sums of the EG1 matrix coefficients.

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