A384809
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^2)^2 ).
Original entry on oeis.org
1, 1, 5, 25, 153, -799, -82787, -2990343, -98020367, -2473062911, -22379003019, 3535310560409, 426542722323721, 33942691393940577, 2320589389274335117, 131491185267395291641, 4583444982950062321377, -254657491559719266483967, -86887910247671284788294683
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
A384813
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384810.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 37, 0, 1, 4, 21, 104, 417, 0, 1, 5, 32, 207, 1280, 4761, 0, 1, 6, 45, 352, 2769, 17392, 33313, 0, 1, 7, 60, 545, 5088, 42363, 213688, -1509339, 0, 1, 8, 77, 792, 8465, 85344, 656505, -472456, -135791359, 0, 1, 9, 96, 1099, 13152, 153325, 1521904, 6181815, -254502688, -8149132943, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 5, 12, 21, 32, 45, ...
0, 37, 104, 207, 352, 545, ...
0, 417, 1280, 2769, 5088, 8465, ...
0, 4761, 17392, 42363, 85344, 153325, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-3*n+3*j+k)^(j-1)*binomial(n, j)*b(n-j, 2*j)));
a(n, k) = b(n, -k);
A384860
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384856.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 28, 0, 1, 4, 27, 98, -107, 0, 1, 5, 40, 216, 304, -11744, 0, 1, 6, 55, 388, 1485, -20638, -519101, 0, 1, 7, 72, 620, 3712, -20592, -1185920, -12366080, 0, 1, 8, 91, 918, 7285, -3836, -1908657, -35662030, -101065751, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 7, 16, 27, 40, 55, ...
0, 28, 98, 216, 388, 620, ...
0, -107, 304, 1485, 3712, 7285, ...
0, -11744, -20638, -20592, -3836, 39200, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*j+k)^(j-1)*binomial(n, j)*b(n-j, 3*j)));
a(n, k) = b(n, -k);
Showing 1-3 of 3 results.