A384617
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^2 ).
Original entry on oeis.org
1, 1, 5, 13, -63, -2279, -51167, -423387, 13717889, 885044593, 37051519041, 779965433149, -14179999608959, -2798466635425239, -224720509492366495, -11148988922254048619, -300176114650473574143, 18804123010954180467937, 4351564646569010083711105
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+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);
A384859
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 A384855.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 10, 0, 1, 4, 27, 62, -503, 0, 1, 5, 40, 162, -632, -8564, 0, 1, 6, 55, 316, -135, -20758, -103751, 0, 1, 7, 72, 530, 1264, -31572, -413900, 3479554, 0, 1, 8, 91, 810, 3865, -34316, -919647, 2636678, 327940225, 0, 1, 9, 112, 1162, 7992, -20500, -1552472, -5475222, 679001872, 8613464536, 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, 10, 62, 162, 316, 530, ...
0, -503, -632, -135, 1264, 3865, ...
0, -8564, -20758, -31572, -34316, -20500, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+j+k)^(j-1)*binomial(n, j)*b(n-j, 3*j)));
a(n, k) = b(n, -k);
Showing 1-3 of 3 results.