A384976
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384951.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 3, 0, 1, 4, 9, 10, 5, 0, 1, 5, 14, 22, 20, 6, 0, 1, 6, 20, 40, 51, 34, 2, 0, 1, 7, 27, 65, 105, 105, 45, -20, 0, 1, 8, 35, 98, 190, 248, 188, 18, -102, 0, 1, 9, 44, 140, 315, 501, 526, 255, -175, -312, 0, 1, 10, 54, 192, 490, 912, 1200, 956, 63, -836, -795, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 5, 9, 14, 20, 27, ...
0, 3, 10, 22, 40, 65, 98, ...
0, 5, 20, 51, 105, 190, 315, ...
0, 6, 34, 105, 248, 501, 912, ...
0, 2, 45, 188, 526, 1200, 2408, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+j+k-1, j-1)*b(n-j, j)/j));
a(n, k) = b(n, -k);
A385014
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^2.
Original entry on oeis.org
1, 1, 3, 4, 3, -15, -118, -336, -595, 1467, 20391, 96205, 353686, 574786, -2717256, -30598208, -197828371, -841728699, -2599029153, -1309899955, 56975269295, 522707807733, 3425068059553, 16747743739845, 63468629516172, 111911654532374, -907903172853988, -12555837715110897
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+j+k-1, j-1)*a(n-j, 2*j)/j));
A385015
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^3.
Original entry on oeis.org
1, 1, 4, 4, -13, -81, -389, -198, 7455, 44515, 198661, 70243, -5428624, -40239313, -218619844, -408542577, 3648305171, 44441073999, 339489511573, 1430556904456, 2122222427956, -35048613488679, -504238969376070, -3684488832562182, -21342732340391295, -67688326964892247
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+j+k-1, j-1)*a(n-j, 3*j)/j));
A385016
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^4.
Original entry on oeis.org
1, 1, 5, 3, -51, -190, -401, 3672, 51925, 151539, -482538, -9063614, -79813421, -183787112, 1737820084, 22402935304, 179028179329, 459719628273, -4012720499801, -61168331089037, -556435825634630, -2299434933774430, 2674772917888194, 157684497102084776
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+j+k-1, j-1)*a(n-j, 4*j)/j));
A385013
G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)^2).
Original entry on oeis.org
1, 1, 2, 4, 9, 19, 37, 52, -25, -630, -3616, -15897, -61476, -215135, -677464, -1823081, -3389900, 2523349, 73121734, 526205851, 2914005085, 14163375846, 62788424920, 255900158756, 945473736954, 3008738746058, 6827204137454, -2853842162077, -171206510083289
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-2*n+2*j+k-1, j-1)*a(n-j, j)/j));
Showing 1-5 of 5 results.