A384719
E.g.f. A(x) satisfies A(x) = exp( x * A(x*A(x))^2 ).
Original entry on oeis.org
1, 1, 5, 61, 1281, 39641, 1655713, 88312869, 5792082817, 454510418545, 41802078248001, 4434246169988669, 535583662477158529, 72887981688629021097, 11079094119653898282337, 1867050981690536859738901, 346619463962928284995333377, 70501622878003227432547203809
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, 2*j)));
A384722
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 A384720.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 118, 0, 1, 4, 27, 278, 3385, 0, 1, 5, 40, 486, 8008, 141556, 0, 1, 6, 55, 748, 14121, 333482, 7918489, 0, 1, 7, 72, 1070, 22000, 587268, 18524980, 561302470, 0, 1, 8, 91, 1458, 31945, 916084, 32452353, 1303041350, 48589734337, 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, 118, 278, 486, 748, 1070, ...
0, 3385, 8008, 14121, 22000, 31945, ...
0, 141556, 333482, 587268, 916084, 1334900, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
Showing 1-2 of 2 results.