A395148 - OEIS

A395148

Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where A(n,k) = (2*n)! * [x^(2*n)] 1/(1 - x^2)^(k/2).

1, 1, 0, 1, 1, 0, 1, 2, 9, 0, 1, 3, 24, 225, 0, 1, 4, 45, 720, 11025, 0, 1, 5, 72, 1575, 40320, 893025, 0, 1, 6, 105, 2880, 99225, 3628800, 108056025, 0, 1, 7, 144, 4725, 201600, 9823275, 479001600, 18261468225, 0, 1, 8, 189, 7200, 363825, 21772800, 1404728325, 87178291200, 4108830350625, 0

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OFFSET

0,8

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).

FORMULA

A(0,k) = 1 and A(n,k) = k*(k+2) * A(n-1,k+4) - k*(k+1) * A(n-1,k+2) for n > 0.

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, ...

0, 1, 2, 3, 4, 5, ...

0, 9, 24, 45, 72, 105, ...