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

0,6

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.

Links

Table of n, a(n) for n=0..44.

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.

Example

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).

Sequence in context: A035237 A189423 A342287 * A138542 A057862 A265512

Adjacent sequences: A230693 A230694 A230695 * A230697 A230698 A230699

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Oct 27 2013

Status

approved