A384897
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^2)^3.
Original entry on oeis.org
1, 1, 3, 3, -8, -81, -462, -1140, 1662, 42210, 341922, 1588428, 3968106, -17035461, -330216303, -2645037192, -15366663001, -56099904270, 42126523152, 2923843607931, 33032055390075, 253102960693959, 1474460670302136, 5496172108115193, -8530990617203547
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-2*n+3*j+k-1, j-1)*a(n-j, 3*j)/j));
A384903
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384898.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 6, 0, 1, 4, 12, 18, 10, 0, 1, 5, 18, 37, 41, -39, 0, 1, 6, 25, 64, 102, -22, -546, 0, 1, 7, 33, 100, 203, 96, -1074, -3563, 0, 1, 8, 42, 146, 355, 372, -1419, -8332, -18918, 0, 1, 9, 52, 203, 570, 876, -1338, -13974, -48606, -68472, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 7, 12, 18, 25, ...
0, 6, 18, 37, 64, 100, ...
0, 10, 41, 102, 203, 355, ...
0, -39, -22, 96, 372, 876, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-3*n+4*j+k-1,j-1)*b(n-j,3*j)/j));
a(n, k) = b(n, -k);
Showing 1-2 of 2 results.