A384894
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^2.
Original entry on oeis.org
1, 1, 2, 1, -4, -14, -30, 12, 330, 1139, 2226, -2288, -39646, -163742, -410900, -89273, 5352720, 31177720, 114624554, 234094417, -312845870, -5584935715, -32878240028, -127407695297, -315375599410, 24759230680, 6177102106748, 44838273448641, 220383314338200
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+2*j+k-1, j-1)*a(n-j, 2*j)/j));
A384944
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 A384941.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 9, -2, 0, 1, 4, 15, 4, -64, 0, 1, 5, 22, 19, -116, -95, 0, 1, 6, 30, 44, -144, -334, 780, 0, 1, 7, 39, 80, -135, -675, 862, 5230, 0, 1, 8, 49, 128, -75, -1060, 70, 11516, 19228, 0, 1, 9, 60, 189, 51, -1414, -1684, 16953, 59632, -90488, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 4, 9, 15, 22, 30, 39, ...
0, -2, 4, 19, 44, 80, 128, ...
0, -64, -116, -144, -135, -75, 51, ...
0, -95, -334, -675, -1060, -1414, -1644, ...
0, 780, 862, 70, -1684, -4380, -7869, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+2*j+k-1, j-1)*b(n-j, 4*j)/j));
a(n, k) = b(n, -k);
A384945
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 A384942.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 11, -5, 0, 1, 4, 18, 0, -135, 0, 1, 5, 26, 16, -255, -110, 0, 1, 6, 35, 44, -345, -540, 3661, 0, 1, 7, 45, 85, -389, -1230, 5777, 16440, 0, 1, 8, 56, 140, -370, -2100, 5918, 40452, -1375, 0, 1, 9, 68, 210, -270, -3049, 3784, 67356, 86065, -827075, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 5, 11, 18, 26, 35, 45, ...
0, -5, 0, 16, 44, 85, 140, ...
0, -135, -255, -345, -389, -370, -270, ...
0, -110, -540, -1230, -2100, -3049, -3954, ...
0, 3661, 5777, 5918, 3784, -770, -7708, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+2*j+k-1, j-1)*b(n-j, 5*j)/j));
a(n, k) = b(n, -k);
A384946
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 A384943.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 6, 0, 1, 3, 13, -9, 0, 1, 4, 21, -6, -244, 0, 1, 5, 30, 10, -470, -39, 0, 1, 6, 40, 40, -660, -674, 11262, 0, 1, 7, 51, 85, -795, -1824, 19599, 36971, 0, 1, 8, 63, 146, -855, -3384, 24171, 100390, -268890, 0, 1, 9, 76, 224, -819, -5224, 24318, 180627, -268456, -3724293, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 6, 13, 21, 30, 40, 51, ...
0, -9, -6, 10, 40, 85, 146, ...
0, -244, -470, -660, -795, -855, -819, ...
0, -39, -674, -1824, -3384, -5224, -7188, ...
0, 11262, 19599, 24171, 24318, 19590, 9778, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+2*j+k-1, j-1)*b(n-j, 6*j)/j));
a(n, k) = b(n, -k);
Showing 1-4 of 4 results.