A294289 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} 1/(1+x^j) - 1).

1, 1, 0, 1, -1, 0, 1, -1, 3, 0, 1, -1, 1, -13, 0, 1, -1, 1, -1, 73, 0, 1, -1, 1, -7, 25, -501, 0, 1, -1, 1, -7, 73, -241, 4051, 0, 1, -1, 1, -7, 49, -421, 1081, -37633, 0, 1, -1, 1, -7, 49, -181, 2641, -3361, 394353, 0, 1, -1, 1, -7, 49, -301, 1561, -32131, 68881

Offset

0,9

Links

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

Formula

B(j,k) is the coefficient of Product_{i=1..k} 1/(1+x^i).

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

Example

Square array A(n,k) begins:
   1,    1,    1,    1,    1, ...
   0,   -1,   -1,   -1,   -1, ...
   0,    3,    1,    1,    1, ...
   0,  -13,   -1,   -7,   -7, ...
   0,   73,   25,   73,   49, ...
   0, -501, -241, -421, -181, ...

Crossrefs

Columns k=0..5 give A000007, A293125, A294290, A294291, A294292, A294293.

Rows n=0 gives A000012.

Main diagonal gives A294261.

Cf. A294212.

Sequence in context: A048838 A181872 A239264 * A059341 A249442 A334739

Adjacent sequences: A294286 A294287 A294288 * A294290 A294291 A294292

Keyword

sign,tabl

Author

Seiichi Manyama, Oct 27 2017

Status

approved