A384720
E.g.f. A(x) satisfies A(x) = exp( x * A(x*A(x))^3 ).
Original entry on oeis.org
1, 1, 7, 118, 3385, 141556, 7918489, 561302470, 48589734337, 5001284972872, 599865865782481, 82534986682048066, 12863925185682542833, 2248009460254706256460, 436716594440553989797369, 93635975845903995553159126, 22021353830468757164023479169, 5650417076648052544704264390160
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
A384721
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 A384719.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 61, 0, 1, 4, 21, 152, 1281, 0, 1, 5, 32, 279, 3200, 39641, 0, 1, 6, 45, 448, 5937, 98192, 1655713, 0, 1, 7, 60, 665, 9696, 181563, 4053688, 88312869, 0, 1, 8, 77, 936, 14705, 296864, 7430265, 213600200, 5792082817, 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, 61, 152, 279, 448, 665, ...
0, 1281, 3200, 5937, 9696, 14705, ...
0, 39641, 98192, 181563, 296864, 452525, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
Showing 1-2 of 2 results.