A384739
E.g.f. A(x) satisfies A(x) = exp( x * A(x*A(x)^2) ).
Original entry on oeis.org
1, 1, 3, 28, 461, 11776, 421207, 19832128, 1179482201, 85990657024, 7513043962571, 772836266189824, 92270347493126629, 12636256749099114496, 1965364897138717976735, 344225592620170387849216, 67392512492360201909759153, 14653181755453024592646111232, 3518079370651785227796264294163
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, (2*n-2*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384742
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 A384740.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 34, 0, 1, 4, 15, 86, 665, 0, 1, 5, 24, 162, 1656, 20556, 0, 1, 6, 35, 268, 3081, 49802, 901417, 0, 1, 7, 48, 410, 5072, 90588, 2132476, 52455250, 0, 1, 8, 63, 594, 7785, 146484, 3792177, 121703094, 3885229665, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 8, 15, 24, 35, ...
0, 34, 86, 162, 268, 410, ...
0, 665, 1656, 3081, 5072, 7785, ...
0, 20556, 49802, 90588, 146484, 221900, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (3*n-3*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Showing 1-2 of 2 results.