

A124216


Generalized Pascal triangle.


2



1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 34, 16, 1, 1, 25, 90, 90, 25, 1, 1, 36, 195, 328, 195, 36, 1, 1, 49, 371, 931, 931, 371, 49, 1, 1, 64, 644, 2240, 3334, 2240, 644, 64, 1, 1, 81, 1044, 4788, 9846, 9846
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OFFSET

0,5


COMMENTS

Consider the 1parameter family of triangles with g.f. (1x(1+y))/(12x(1+y)+x^2(1+k*x+y^2)). A007318 corresponds to k=2. A056241 corresponds to k=1. A124216 corresponds to k=0. Row sums are A006012. Diagonal sums are A124217.


LINKS

Table of n, a(n) for n=0..50.
P. Barry, On a Generalization of the Narayana Triangle, J. Int. Seq. 14 (2011) # 11.4.5


FORMULA

G.f.: (1x(1+y))/(12x(1+y)+x^2(1+y^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j)C(j,2(jk))2^(jk)}.
Equals 2*A001263  A007318; (i.e. twice the Narayana triangle minus Pascal's triangle).  Gary W. Adamson, Jun 14 2007


EXAMPLE

Triangle begins
1,
1, 1,
1, 4, 1,
1, 9, 9, 1,
1, 16, 34, 16, 1,
1, 25, 90, 90, 25, 1,
1, 36, 195, 328, 195, 36, 1,
1, 49, 371, 931, 931, 371, 49, 1


CROSSREFS

Cf. A001263.
Sequence in context: A082043 A177944 A174006 * A008459 A259333 A180960
Adjacent sequences: A124213 A124214 A124215 * A124217 A124218 A124219


KEYWORD

easy,nonn,tabl


AUTHOR

Paul Barry, Oct 19 2006


STATUS

approved



