A384740
E.g.f. A(x) satisfies A(x) = exp( x * A(x*A(x)^3) ).
Original entry on oeis.org
1, 1, 3, 34, 665, 20556, 901417, 52455250, 3885229665, 355223077336, 39166024398641, 5113078496932374, 778733373110049601, 136679150176555902436, 27360426865918664532393, 6191378995818235673842546, 1571577905668087973855557313, 444441393534829346316950781744
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, (3*n-3*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384741
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 A384739.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 28, 0, 1, 4, 15, 74, 461, 0, 1, 5, 24, 144, 1200, 11776, 0, 1, 6, 35, 244, 2325, 29842, 421207, 0, 1, 7, 48, 380, 3968, 56688, 1040896, 19832128, 0, 1, 8, 63, 558, 6285, 95524, 1933227, 47948490, 1179482201, 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, 28, 74, 144, 244, 380, ...
0, 461, 1200, 2325, 3968, 6285, ...
0, 11776, 29842, 56688, 95524, 150400, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (2*n-2*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Showing 1-2 of 2 results.