

A099557


Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x).


2



1, 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 4, 3, 1, 0, 1, 5, 6, 4, 0, 0, 1, 6, 10, 10, 1, 0, 0, 1, 7, 15, 20, 5, 1, 0, 0, 1, 8, 21, 35, 15, 6, 0, 0, 0, 1, 9, 28, 56, 35, 21, 1, 0, 0, 0, 1, 10, 36, 84, 70, 56, 7, 1, 0, 0, 0, 1, 11, 45, 120, 126, 126, 28, 8, 0, 0, 0, 0
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OFFSET

0,5


COMMENTS

Row sums form A005314. Antidiagonal sums form A099558.


LINKS

Table of n, a(n) for n=0..77.


FORMULA

G.f.: (1x+x*y)/((1x)^2x^3*y^2).


EXAMPLE

Rows begin:
[1],
[1,1],
[1,2,0],
[1,3,1,0],
[1,4,3,1,0],
[1,5,6,4,0,0],
[1,6,10,10,1,0,0],
[1,7,15,20,5,1,0,0],
[1,8,21,35,15,6,0,0,0],
[1,9,28,56,35,21,1,0,0,0],
[1,10,36,84,70,56,7,1,0,0,0],...
and can be derived from Pascal's triangle
by shifting each column k down by [k/2] rows.


PROG

(PARI) {T(n, k)=polcoeff(polcoeff((1x+x*y)/((1x)^2x^3*y^2)+x*O(x^n), n, x)+y*O(y^k), k, y)}


CROSSREFS

Cf. A005314, A099558.
Sequence in context: A174067 A124943 A169803 * A214576 A079217 A079221
Adjacent sequences: A099554 A099555 A099556 * A099558 A099559 A099560


KEYWORD

nonn,tabl


AUTHOR

Paul D. Hanna, Oct 22 2004


STATUS

approved



