A395141 - OEIS

A395141

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)^3 dx ).

1, 1, 0, 1, 1, 0, 1, 2, 13, 0, 1, 3, 32, 493, 0, 1, 4, 57, 1376, 37369, 0, 1, 5, 88, 2739, 114176, 4732249, 0, 1, 6, 125, 4672, 246801, 15519488, 901188997, 0, 1, 7, 168, 7265, 454144, 35822307, 3132551168, 240798388357, 0, 1, 8, 217, 10608, 757625, 70084096, 7636142793, 879422726144, 85948640603761, 0

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OFFSET

0,8

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(0,k) = 1 and A(n,k) = k*(k+3) * A(n-1,k+6) - k*(k+2) * A(n-1,k+4) for n > 0.

EXAMPLE

Square array begins:

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

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

0, 13, 32, 57, 88, 125, ...