OFFSET
0,3
COMMENTS
The even-indexed rows (at least if limited to k<=1+n/2) are left-right symmetric.
LINKS
G. C. Greubel, Rows n=0..100 of triangle, flattened
EXAMPLE
1, 1;
2, 6;
3, 18, 3;
4, 40, 20;
5, 75, 75, 5;
6, 126, 210, 42;
7, 196, 490, 196, 7;
8, 288, 1008, 672, 72;
9, 405, 1890, 1890, 405, 9;
10, 550, 3300, 4620, 1650, 110;
11, 726, 5445, 10164, 5445, 726, 11;
MAPLE
A178667 := proc(n, k)
(-1)^n*(x-1)^(n+2)*add(x^j/Beta(n+1, 2*j+1), j=0..n+1) ;
coeftayl(%, x=0, k) ;
end proc: # R. J. Mathar, Feb 12 2013
MATHEMATICA
p[x_, n_] = (-1)^n*(-1 + x)^(n + 2)*Sum[(1/Beta[n + 1, 2*k + 1])x^k, {k, 0, Infinity}];
Flatten[Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Jun 02 2010
STATUS
approved