cp's OEIS Frontend

Examples

			Coefficients in the n-th row g.f., R(n,x), of this table begins:
n=0: [1, 1,-2,  9, -56,  425, -3726,  36652, -397440, 4695489, ...];
n=1: [1, 1,-1,  3, -13,   71,  -461,   3447,  -29093,  273343, ...];
n=2: [1, 1, 0,  0,   0,    0,     0,      0,       0,       0, ...];
n=3: [1, 1, 1,  0,  -1,    1,     0,      0,      -5,      27, ...];
n=4: [1, 1, 2,  3,   0,  -12,   -14,     43,      96,     -50, ...];
n=5: [1, 1, 3,  9,  19,    0,  -195,   -732,    -453,    6495, ...];
n=6: [1, 1, 4, 18,  72,  201,     0,  -4200,  -27984,  -91044, ...];
n=7: [1, 1, 5, 30, 175,  880,  3106,      0, -114485,-1124735, ...];
n=8: [1, 1, 6, 45, 344, 2451, 14946,  64522,       0,-3805692, ...];
n=9: [1, 1, 7, 63, 595, 5453, 45927, 331177, 1704795,       0, ...];
n=10:[1, 1, 8, 84, 944,10550,112336,1094604, 9157984,55095601, 0,...]; ...
in which the main diagonal is zeros for n>=2.
Initial row g.f.s are illustrated by the following.
R(0,x) = 1 + x*[d/dx x/R(0,x)] begins:
R(0,x) = 1 + x - 2*x^2 + 9*x^3 - 56*x^4 + 425*x^5 - 3726*x^6 +...
which satisfies: [x^k] R(0,x)^(k+1) = [x^k] R(0,x)^k for k>=2.
...
R(1,x) = 1 + x*R(1,x)*[d/dx x/R(1,x)] begins:
R(1,x) = 1 + x - x^2 + 3*x^3 - 13*x^4 + 71*x^5 - 461*x^6 + 3447*x^7 +...
which satisfies: [x^k] R(1,x)^k = [x^k] R(1,x)^(k-1) for k>=2.
...
R(2,x) = 1 + x*R(2,x)^2*[d/dx x/R(2,x)] is satisfied by:
R(2,x) = 1 + x,
which satisfies: [x^k] R(2,x)^(k-1) = [x^k] R(2,x)^(k-2) = 0 for k>=2.
...
R(3,x) = 1 + x*R(3,x)^3*[d/dx x/R(3,x)] begins:
R(3,x) = 1 + x + x^2 - x^4 + x^5 - 5*x^8 + 27*x^9 - 147*x^10 + 996*x^11 +...
which satisfies: [x^k] R(3,x)^(k-2) = [x^k] R(3,x)^(k-3) for k>=2.
...