A384810
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^2 ).
Original entry on oeis.org
1, 1, 5, 37, 417, 4761, 33313, -1509339, -135791359, -8149132943, -455269648959, -24532196772291, -1260399381304511, -56411711489070807, -1357347436103060191, 146282852689561868821, 35003916010171558562817, 5112183093788001812407521, 647998390863196992450043777
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-3*n+3*j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
A384861
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 A384857.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 46, 0, 1, 4, 27, 134, 361, 0, 1, 5, 40, 270, 1384, -6284, 0, 1, 6, 55, 460, 3321, -2518, -632951, 0, 1, 7, 72, 710, 6448, 18468, -1223180, -31583474, 0, 1, 8, 91, 1026, 11065, 65524, -1591407, -72713338, -1484748191, 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, 46, 134, 270, 460, 710, ...
0, 361, 1384, 3321, 6448, 11065, ...
0, -6284, -2518, 18468, 65524, 149300, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-3*n+3*j+k)^(j-1)*binomial(n, j)*b(n-j, 3*j)));
a(n, k) = b(n, -k);
Showing 1-2 of 2 results.