A059587 T(n,m) = (1/m!)*Sum_{i=0..m} stirling1(m,i)*(2^i)*(2^i+1)*...*(2^i+n-1).
1, 1, 1, 2, 1, 2, 6, 7, 4, 1, 6, 24, 48, 68, 73, 56, 28, 8, 1, 24, 120, 360, 940, 2251, 4704, 8176, 11488, 12876, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 120, 720, 3000, 12720, 56660, 247016, 987252, 3480536, 10647035, 28163200, 64592320, 129068160
Offset: 0
Examples
Triangle starts: 1, 1; 1, 2, 1; 2, 6, 7, 4, 1; 6, 24, 48, 68, 73, 56, 28, 8, 1; ...
Programs
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Maple
with(combinat): for n from 0 to 10 do for m from 0 to 2^n do printf(`%d,`,sum(abs(stirling1(n,i))*binomial(2^i, m), i=0..n)) od: od:
Formula
T(n, m) = Sum_{i=0..n} |stirling1(n, i)|*binomial(2^i, m).
Extensions
More terms from James Sellers, Jan 24 2001