A384860
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 A384856.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 28, 0, 1, 4, 27, 98, -107, 0, 1, 5, 40, 216, 304, -11744, 0, 1, 6, 55, 388, 1485, -20638, -519101, 0, 1, 7, 72, 620, 3712, -20592, -1185920, -12366080, 0, 1, 8, 91, 918, 7285, -3836, -1908657, -35662030, -101065751, 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, 28, 98, 216, 388, 620, ...
0, -107, 304, 1485, 3712, 7285, ...
0, -11744, -20638, -20592, -3836, 39200, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*j+k)^(j-1)*binomial(n, j)*b(n-j, 3*j)));
a(n, k) = b(n, -k);
A384855
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^3 ).
Original entry on oeis.org
1, 1, 7, 10, -503, -8564, -103751, 3479554, 327940225, 8613464536, -36391967279, -24834942253274, -2356662167845487, -88482481533921500, 1825569695231959993, 704791058412273699106, 88829364712362626504449, 5460031123686211024338736, 23871425875449192877470625
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
A384857
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^3 ).
Original entry on oeis.org
1, 1, 7, 46, 361, -6284, -632951, -31583474, -1484748191, -51928436312, -303653774159, 219248741052826, 35743757192135425, 4097960104621191004, 408462300514973323753, 33384541884258873033406, 1521231207001104466842049, -200132739000502301652035888, -84772475888572203988197350303
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, 3*j)));
A384858
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^8)^3 ).
Original entry on oeis.org
1, 1, 7, 136, 3781, 163216, 9103699, 646696576, 55084545289, 5491386074368, 625131329307391, 79898089652402176, 11312691034562944525, 1755128489880477528064, 295767148537661982373963, 53734366029378178883731456, 10459045695948264117117132049, 2169330513346145105101803814912
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-8*n+8*j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
Showing 1-4 of 4 results.