A384862
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 A384858.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 136, 0, 1, 4, 27, 314, 3781, 0, 1, 5, 40, 540, 8944, 163216, 0, 1, 6, 55, 820, 15741, 383282, 9103699, 0, 1, 7, 72, 1160, 24448, 672768, 21329920, 646696576, 0, 1, 8, 91, 1566, 35365, 1045924, 37392543, 1504825562, 55084545289, 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, 136, 314, 540, 820, 1160, ...
0, 3781, 8944, 15741, 24448, 35365, ...
0, 163216, 383282, 672768, 1045924, 1518800, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-8*n+8*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)));
A384856
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^2)^3 ).
Original entry on oeis.org
1, 1, 7, 28, -107, -11744, -519101, -12366080, -101065751, 19899785728, 2369020104991, 160985802059776, 8664193820140093, 137309806362677248, -48557247646714851365, -9196626471351773732864, -1230646715294157585659951, -124354471985557029636669440, -8657982884640209349171498569
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*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)));
Showing 1-4 of 4 results.