A230696 Triangle read by rows related to double factorial of odd numbers (A001147).

1, 0, 1, 1, 0, 2, 0, 11, 0, 4, 25, 0, 72, 0, 8, 0, 589, 0, 340, 0, 16, 2025, 0, 7010, 0, 1328, 0, 32, 0, 75319, 0, 55160, 0, 4592, 0, 64, 342225, 0, 1335328, 0, 334752, 0, 14592, 0, 128

Offset: 0

Author

Philippe Deléham, Oct 27 2013

Keywords

• easy
• nonn
• tabl

Comments

The row polynomials t(n,x):= sum(T(n,k)*x^k, k=0..n) satisfy the recurrence relation t(n,x) = 2x*t(n-1,x) + ((2n-3)^2)*t(n-2,x); t(0,x) = 1, t(1,x) = x.

Examples

			Triangle begins:
1
0, 1
1, 0, 2
0, 11, 0, 4
25, 0, 72, 0, 8
0, 589, 0, 340, 0, 16
2025, 0, 7010, 0, 1328, 0, 32
0, 75319, 0, 55160, 0, 4592, 0, 64
		

Crossrefs

T(2n,0) = A007696(n)^2.

T(n,n) = A011782(n).

A001147 (row sums).

Cf. A060524 (similar sequence).

Formula

T(n,k) = 2*T(n-1,k-1) + ((2n-3)^2)*T(n-2,k); T(0,0) = 1, T(1,0) = 0, T(1,1) = 1, T(n,k) = 0 if k>n or if k<0.