A355609 - OEIS

A355609

Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 - x)^(-x^k).

1, 1, 1, 1, 0, 2, 1, 0, 2, 6, 1, 0, 0, 3, 24, 1, 0, 0, 6, 20, 120, 1, 0, 0, 0, 12, 90, 720, 1, 0, 0, 0, 24, 40, 594, 5040, 1, 0, 0, 0, 0, 60, 540, 4200, 40320, 1, 0, 0, 0, 0, 120, 240, 3528, 34544, 362880, 1, 0, 0, 0, 0, 0, 360, 1260, 25200, 316008, 3628800, 1, 0, 0, 0, 0, 0, 720, 1680, 28224, 263520, 3207240, 39916800

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OFFSET

0,6

LINKS

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

FORMULA

T(0,k) = 1 and T(n,k) = (n-1)! * Sum_{j=k+1..n} j/(j-k) * T(n-j,k)/(n-j)! for n > 0.

T(n,k) = n! * Sum_{j=0..floor(n/(k+1))} |Stirling1(n-k*j,j)|/(n-k*j)!.

EXAMPLE

Square array begins:

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

1, 0, 0, 0, 0, 0, 0, ...