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

2,1

Comments

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.

Links

Table of n, a(n) for n=2..24.

Formula

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.

Crossrefs

Equals (2*n-1)*A052468(n-1)

Cf. A162440 and A162442 [denom(cs(n))].

Cf. A161739 (RSEG2 triangle), A001803 and A046161.

Sequence in context: A019009 A290716 A347998 * A001803 A161738 A062741

Adjacent sequences: A162438 A162439 A162440 * A162442 A162443 A162444

Keyword

easy,frac,nonn

Author

Johannes W. Meijer, Jul 06 2009

Status

approved