A395146 - OEIS

A395146

Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where A(n,k) = (2*n)! * [x^(2*n)] C(x)^k and C(x) satisfies C(x) = cosh( Integral C(x)^4 dx ).

1, 1, 0, 1, 1, 0, 1, 2, 17, 0, 1, 3, 40, 865, 0, 1, 4, 69, 2240, 88865, 0, 1, 5, 104, 4215, 246400, 15335425, 0, 1, 6, 145, 6880, 494025, 44844800, 3993275825, 0, 1, 7, 192, 10325, 855680, 94528875, 12197785600, 1462392957025, 0, 1, 8, 245, 14640, 1357825, 171673600, 26798419725, 4635158528000, 716611617346625, 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+4) * A(n-1,k+8) - k*(k+3) * A(n-1,k+6) for n > 0.

EXAMPLE

Square array begins:

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

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

0, 17, 40, 69, 104, 145, ...