A113408 Riordan array (1/(1-x^2-x^4*c(x^4)),x*c(x^2)), c(x) the g.f. of A000108.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 3, 0, 1, 0, 6, 0, 4, 0, 1, 3, 0, 12, 0, 5, 0, 1, 0, 12, 0, 20, 0, 6, 0, 1, 6, 0, 30, 0, 30, 0, 7, 0, 1, 0, 30, 0, 60, 0, 42, 0, 8, 0, 1, 10, 0, 90, 0, 105, 0, 56, 0, 9, 0, 1, 0, 60, 0, 210, 0, 168, 0, 72, 0, 10, 0, 1, 20, 0, 210, 0, 420, 0, 252, 0, 90, 0, 11, 0, 1

Offset: 0

Author

Paul Barry, Oct 28 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A113409. Diagonal sums are A005773(n+1) with interpolated zeros.

Examples

			Triangle begins
1;
0,1;
1,0,1;
0,2,0,1;
2,0,3,0,1;
0,6,0,4,0,1;
3,0,12,0,5,0,1;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Programs

Mathematica

Table[Binomial[(n + k)/2, k]*Binomial[Floor[(n - k)/2], Floor[(n - k)/4]]*(1 + (-1)^(n - k))/2, {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 09 2017 *)

PARI

for(n=0,25, for(k=0,n, print1( binomial((n+k)/2,k) *binomial(floor((n-k)/2),floor((n-k)/4))*(1+(-1)^(n-k))/2, ", "))) \\ G. C. Greubel, Mar 09 2017

Formula

T(n, k) = C((n+k)/2,k)*C(floor((n-k)/2),floor((n-k)/4))(1+(-1)^(n-k))/2.