OFFSET
0,4
LINKS
Gheorghe Coserea, Rows n=0..123, flattened
Luca G. Molinari, Nicola Manini, Enumeration of many-body skeleton diagrams, arXiv:cond-mat/0512342 [cond-mat.str-el], 2006.
FORMULA
EXAMPLE
A(x;t) = 1 + (1 + t)*x + (4 + 5*t + t^2)*x^2 + (27 + 40*t + 14*t^2 + t^3)*x^3 + ...
Triangle starts:
n\k [0] [1] [2] [3] [4] [5] [6] [7] [8]
[0] 1;
[1] 1; 1;
[2] 4, 5, 1;
[3] 27, 40, 14, 1;
[4] 248, 419, 200, 30, 1;
[5] 2830, 5308, 3124, 700, 55, 1;
[6] 38232, 78070, 53620, 15652, 1960, 91, 1;
[7] 593859, 1301088, 1007292, 356048, 60550, 4704, 140, 1;
[8] 10401712, 24177939, 20604768, 8430844, 1787280, 194854, 10080, 204, 1;
[9] ...
MATHEMATICA
max = 11; y0[x_, t_] = 1; y1[x_, t_] = 0; For[n = 1, n <= max, n++, y1[x_, t_] = Normal[(1 + x*(1 + 2*t + x*t^2)*y0[x, t]^2 + t*(1 - t)*x^2*y0[x, t]^3 + 2*x^2*y0[x, t]*D[y0[x, t], x])/(1 + 2*x*t) + O[x]^n]; y0[x_, t_] = y1[x, t]];
row[n_] := CoefficientList[SeriesCoefficient[y0[x, t]/(1 - x*t*y0[x, t]), {x, 0, n}], t];
Flatten[Table[row[n], {n, 0, max-1}]] (* Jean-François Alcover, May 23 2017, adapted from PARI *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gheorghe Coserea, May 21 2017
STATUS
approved