A381425 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of (1 + x/(1-x)^k)^k.
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 5, 1, 0, 1, 4, 12, 10, 1, 0, 1, 5, 22, 37, 18, 1, 0, 1, 6, 35, 92, 102, 30, 1, 0, 1, 7, 51, 185, 345, 258, 47, 1, 0, 1, 8, 70, 326, 880, 1188, 606, 70, 1, 0, 1, 9, 92, 525, 1881, 3851, 3796, 1335, 100, 1, 0, 1, 10, 117, 792, 3563, 10002, 15655, 11364, 2781, 138, 1, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, 1, ... 0, 1, 2, 3, 4, 5, 6, ... 0, 1, 5, 12, 22, 35, 51, ... 0, 1, 10, 37, 92, 185, 326, ... 0, 1, 18, 102, 345, 880, 1881, ... 0, 1, 30, 258, 1188, 3851, 10002, ... 0, 1, 47, 606, 3796, 15655, 49468, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Crossrefs
Programs
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PARI
a(n, k) = sum(j=0, k, binomial(k, j)*binomial(n+(k-1)*j-1, n-j));
Formula
A(n,k) = Sum_{j=0..k} binomial(k,j) * binomial(n+(k-1)*j-1,n-j).