A384901
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 A384896.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 0, 0, 1, 4, 12, 6, -23, 0, 1, 5, 18, 19, -37, -51, 0, 1, 6, 25, 40, -33, -148, 27, 0, 1, 7, 33, 70, -1, -264, -186, 920, 0, 1, 8, 42, 110, 70, -360, -681, 1588, 5469, 0, 1, 9, 52, 161, 192, -384, -1446, 1437, 13469, 4836, 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, 0, 6, 19, 40, 70, ...
0, -23, -37, -33, -1, 70, ...
0, -51, -148, -264, -360, -384, ...
-
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,3*j)/j));
a(n, k) = b(n, -k);
A384941
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^4.
Original entry on oeis.org
1, 1, 4, -2, -64, -95, 780, 5230, 19228, -90488, -1454232, -4080620, 19557280, 270109125, 1702743364, -35378580, -74674412048, -515950535521, -1719717134140, 9100931191804, 173629815007712, 988336433707663, 2065106985108344, -25897495149473592
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, 4*j)/j));
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));
A384898
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 3, 6, 10, -39, -546, -3563, -18918, -68472, -47978, 2060310, 25856241, 210422728, 1367033271, 6837535155, 18339297562, -114989342976, -2525856651999, -27658429475813, -235591084478085, -1658029364805855, -9188248947018893, -28582654956147315, 177119046663378954
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-3*n+4*j+k-1, j-1)*a(n-j, 3*j)/j));
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));
A385015
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^3.
Original entry on oeis.org
1, 1, 4, 4, -13, -81, -389, -198, 7455, 44515, 198661, 70243, -5428624, -40239313, -218619844, -408542577, 3648305171, 44441073999, 339489511573, 1430556904456, 2122222427956, -35048613488679, -504238969376070, -3684488832562182, -21342732340391295, -67688326964892247
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, 3*j)/j));
Showing 1-7 of 7 results.