0,13

Columns include A005043, A001006, A002026. Row sums are A124791. For even k, column k has g.f. x^k*M(x)^(k/2), where M(x)=2/(1-x+sqrt(1-2x-3x^2)) is the g.f. of A001006. For odd k, column k has g.f. x^k*S(x)*M(x)^floor(k/2), S(x)=(1+x-sqrt(1-2x-3x^2))/(2x(1+x)), the g.f. of A005043.

Triangle is the product of A124788 and A124305, that is, it is the product of the expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2) and the inverse of the Riordan array (1,x(1-x^2)).

Triangle begins

1,

0, 1,

0, 0, 1,

0, 1, 1, 1,

0, 1, 2, 1, 1,

0, 3, 4, 3, 2, 1,

0, 6, 9, 6, 5, 2, 1,

0, 15, 21, 15, 12, 6, 3, 1,

0, 36, 51, 36, 30, 15, 9, 3, 1,

0, 91, 127, 91, 76, 40, 25, 10, 4, 1,

0, 232, 323, 232, 196, 105, 69, 29, 14, 4, 1

Sequence in context: A111571 A051509 A124816 this_sequence A135221 A106234 A062507

Adjacent sequences: A124787 A124788 A124789 this_sequence A124791 A124792 A124793

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Nov 07 2006