A384951
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)).
Original entry on oeis.org
1, 1, 2, 3, 5, 6, 2, -20, -102, -312, -795, -1483, -1102, 7035, 51059, 219453, 779078, 2307104, 5508377, 7633065, -19349069, -226127800, -1296826960, -5855601434, -22970901723, -78578482054, -224208769108, -429111559993, 429212740026, 10534398465308
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+j+k-1, j-1)*a(n-j, j)/j));
A385017
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 A385013.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 4, 0, 1, 4, 9, 12, 9, 0, 1, 5, 14, 25, 30, 19, 0, 1, 6, 20, 44, 69, 72, 37, 0, 1, 7, 27, 70, 133, 183, 164, 52, 0, 1, 8, 35, 104, 230, 384, 464, 326, -25, 0, 1, 9, 44, 147, 369, 716, 1060, 1083, 435, -630, 0, 1, 10, 54, 200, 560, 1230, 2125, 2748, 2139, -464, -3616, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 5, 9, 14, 20, 27, ...
0, 4, 12, 25, 44, 70, 104, ...
0, 9, 30, 69, 133, 230, 369, ...
0, 19, 72, 183, 384, 716, 1230, ...
0, 37, 164, 464, 1060, 2125, 3893, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-2*n+2*j+k-1, j-1)*b(n-j, j)/j));
a(n, k) = b(n, -k);
Showing 1-2 of 2 results.
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