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Triangle of coefficients of quasi-Stirling polynomials.
1

%I #15 Feb 05 2020 10:13:20

%S 1,1,3,1,13,16,1,39,171,125,1,101,1091,2551,1296,1,243,5498,28838,

%T 43653,16807,1,561,24270,243790,780585,850809,262144,1,1263,98661,

%U 1733035,10073955,22278189,18689527,4782969,1,2797,379693,10996369,106215619,410994583,677785807,457947691,100000000

%N Triangle of coefficients of quasi-Stirling polynomials.

%H Sergi Elizalde, <a href="https://arxiv.org/abs/2002.00985">Descents on quasi-Stirling permutations</a>, arXiv:2002.00985 [math.CO], 2020. See p. 7.

%e Triangle begins

%e 1;

%e 1, 3;

%e 1, 13, 16;

%e 1, 39, 171, 125;

%e 1, 101, 1091, 2551, 1296;

%e 1, 243, 5498, 28838, 43653, 16807;

%o (PARI)

%o A(t, z) = (1-t)/(1 - t*exp((1-t)*z));

%o Q(n, t) = (n!/(n+1))*polcoeff(A(t, z)^(n+1), n, z);

%o row(n) = my(rowx = Vec(Q(n, t))); vector(n, k, rowx[k]);

%K nonn,tabl

%O 1,3

%A _Michel Marcus_, Feb 05 2020