A362277 - OEIS

A362277

Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j * binomial(n-j,j)/(n-j)!.

1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, -1, -2, 1, 1, 1, -2, -5, -2, 1, 1, 1, -3, -8, 1, 6, 1, 1, 1, -4, -11, 10, 41, 16, 1, 1, 1, -5, -14, 25, 106, 31, -20, 1, 1, 1, -6, -17, 46, 201, -44, -461, -132, 1, 1, 1, -7, -20, 73, 326, -299, -1952, -895, 28, 1, 1, 1, -8, -23, 106, 481, -824, -5123, -1028, 6481, 1216, 1

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OFFSET

0,14

LINKS

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

FORMULA

E.g.f. of column k: exp(x - k*x^2/2).

T(n,k) = T(n-1,k) - k*(n-1)*T(n-2,k) for n > 1.

T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j / (j! * (n-2*j)!).

EXAMPLE

Square array begins:

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