|
| |
|
|
A162441
|
|
Numerators of the column sums of the EG1 matrix coefficients
|
|
2
|
|
|
|
3, 15, 35, 315, 693, 1001, 6435, 109395, 230945, 969969, 2028117, 16900975, 35102025, 145422675, 20036013, 9917826435, 20419054425, 27981667175, 172308161025, 282585384081, 964378691705, 11835556670925, 24185702762325
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
