A293991 - OEIS

A293991

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Sum_{j=1..k+1} binomial(k,j-1)*x^j/j).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 1, 1, 4, 9, 10, 1, 1, 1, 5, 16, 33, 26, 1, 1, 1, 6, 25, 76, 141, 76, 1, 1, 1, 7, 36, 145, 436, 651, 232, 1, 1, 1, 8, 49, 246, 1025, 2776, 3333, 764, 1, 1, 1, 9, 64, 385, 2046, 8245, 19384, 18369, 2620, 1, 1, 1, 10, 81

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OFFSET

0,9

LINKS

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

FORMULA

E.g.f. of column k: exp(((1+x)^(k+1) - 1)/(k+1)).

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

EXAMPLE

Square array A(n,k) begins:

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

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