A369919 Triangular array read by rows. T(n,k) is the number of labeled posets on [n] of rank at most one with exactly k elements of positive indegree, n >= 0, 0 <= k <= max{0,n-1}.
1, 1, 1, 2, 1, 9, 3, 1, 28, 54, 4, 1, 75, 490, 270, 5, 1, 186, 3375, 6860, 1215, 6, 1, 441, 20181, 118125, 84035, 5103, 7, 1, 1016, 111132, 1668296, 3543750, 941192, 20412, 8, 1, 2295, 580644, 21003948, 116363646, 95681250, 9882516, 78732, 9
Offset: 0
Examples
Triangle begins 1; 1; 1, 2; 1, 9, 3; 1, 28, 54, 4; 1, 75, 490, 270, 5; 1, 186, 3375, 6860, 1215, 6; ...
Programs
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Mathematica
nn = 9; Map[Select[#, # > 0 &] &,Table[n!, {n, 0, nn}] CoefficientList[Series[ Sum[ Exp[y x]^(2^n - 1) x^n/n!, {n, 0, nn}], {x, 0, nn}], {x, y}]] // Grid
Formula
E.g.f.: Sum_{n>=0} x^n/n!*exp(y*x)^(2^n-1).
T(n,1) = A058877(n).
Comments