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);
A384942
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^5.
Original entry on oeis.org
1, 1, 5, -5, -135, -110, 3661, 16440, -1375, -827075, -8388505, 2298072, 496514205, 2782147265, 322830120, -164675585390, -1846591014842, -3084367863270, 84920580735040, 845318162940805, 4163798547024100, -18708392155753220, -503209620889452990, -3212928238924865090
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, 5*j)/j));
A384943
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^6.
Original entry on oeis.org
1, 1, 6, -9, -244, -39, 11262, 36971, -268890, -3724293, -24899558, 159971919, 3851093928, 9663394063, -197371002600, -2108992348026, -9447769941412, 111942512192787, 2253965670439788, 7917705821761592, -100488750700889250, -1520857626228210483
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, 6*j)/j));
A385016
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^4.
Original entry on oeis.org
1, 1, 5, 3, -51, -190, -401, 3672, 51925, 151539, -482538, -9063614, -79813421, -183787112, 1737820084, 22402935304, 179028179329, 459719628273, -4012720499801, -61168331089037, -556435825634630, -2299434933774430, 2674772917888194, 157684497102084776
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, 4*j)/j));
Showing 1-4 of 4 results.