A383900 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of Product_{j=0..k} (1 + j*x)/(1 - j*x).
1, 1, 0, 1, 2, 0, 1, 6, 2, 0, 1, 12, 18, 2, 0, 1, 20, 72, 42, 2, 0, 1, 30, 200, 312, 90, 2, 0, 1, 42, 450, 1400, 1152, 186, 2, 0, 1, 56, 882, 4650, 8000, 3912, 378, 2, 0, 1, 72, 1568, 12642, 38250, 40520, 12672, 762, 2, 0, 1, 90, 2592, 29792, 142002, 271770, 190400, 39912, 1530, 2, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 0, 2, 6, 12, 20, 30, ... 0, 2, 18, 72, 200, 450, ... 0, 2, 42, 312, 1400, 4650, ... 0, 2, 90, 1152, 8000, 38250, ... 0, 2, 186, 3912, 40520, 271770, ...
Crossrefs
Programs
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PARI
a(n, k) = sum(j=0, k, abs(stirling(k+1, j+1, 1))*stirling(j+n, k, 2));
Formula
A(n,k) = Sum_{j=0..k} |Stirling1(k+1,j+1)| * Stirling2(j+n,k).