A384691
E.g.f. A(x) satisfies A(x) = exp( x*A(x) * A(x*A(x))^2 ).
Original entry on oeis.org
1, 1, 7, 112, 2989, 115136, 5899159, 381657928, 30082660633, 2814548348224, 306467497027531, 38242238970083336, 5401465336487870533, 854848596955885610560, 150317821473136130378335, 29159232358630752927016456, 6201999009581132843649181489, 1438725999127826885623788697472
Offset: 0
-
terms = 18; A[] = 0; Do[A[x] = Exp[x*A[x]*A[x*A[x]]^2] + O[x]^terms // Normal, terms]; Range[0,terms-1]!CoefficientList[A[x], x] (* Stefano Spezia, Jun 07 2025 *)
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, (n+k)^(j-1)*binomial(n, j)*a(n-j, 2*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)));
A384718
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 A052750.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 49, 0, 1, 4, 21, 128, 729, 0, 1, 5, 32, 243, 2000, 14641, 0, 1, 6, 45, 400, 3993, 41472, 371293, 0, 1, 7, 60, 605, 6912, 85683, 1075648, 11390625, 0, 1, 8, 77, 864, 10985, 153664, 2278125, 33554432, 410338673, 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, 49, 128, 243, 400, 605, ...
0, 729, 2000, 3993, 6912, 10985, ...
0, 14641, 41472, 85683, 153664, 253125, ...
Showing 1-3 of 3 results.