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A230696 Triangle read by rows related to double factorial of odd numbers (A001147). 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A086890 A167387 A189423 * A138542 A057862 A265512

Adjacent sequences:  A230693 A230694 A230695 * A230697 A230698 A230699

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Oct 27 2013

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)