A383843 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/Product_{j=0..k} (1 - j*x)^2.
1, 1, 0, 1, 2, 0, 1, 6, 3, 0, 1, 12, 23, 4, 0, 1, 20, 86, 72, 5, 0, 1, 30, 230, 480, 201, 6, 0, 1, 42, 505, 2000, 2307, 522, 7, 0, 1, 56, 973, 6300, 14627, 10044, 1291, 8, 0, 1, 72, 1708, 16464, 65002, 95060, 40792, 3084, 9, 0, 1, 90, 2796, 37632, 227542, 587580, 567240, 157440, 7181, 10, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, 1, ... 0, 2, 6, 12, 20, 30, 42, ... 0, 3, 23, 86, 230, 505, 973, ... 0, 4, 72, 480, 2000, 6300, 16464, ... 0, 5, 201, 2307, 14627, 65002, 227542, ... 0, 6, 522, 10044, 95060, 587580, 2725380, ... 0, 7, 1291, 40792, 567240, 4817990, 29331038, ...
Crossrefs
Programs
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PARI
a(n, k) = sum(j=0, n, stirling(j+k, k, 2)*stirling(n-j+k, k, 2));
Formula
A(n,k) = Sum_{j=0..n} Stirling2(j+k,k) * Stirling2(n-j+k,k).