A365121
G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^2)^3.
Original entry on oeis.org
1, 3, 9, 40, 192, 993, 5375, 30081, 172650, 1010640, 6010530, 36214656, 220590082, 1356131892, 8403647454, 52436122717, 329170499604, 2077465903503, 13173914483799, 83897445169341, 536355204428412, 3440875097256529, 22144300030907667
Offset: 0
-
a(n, s=2, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365133
G.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^2)^2.
Original entry on oeis.org
1, 2, 9, 48, 284, 1792, 11816, 80446, 561186, 3990398, 28815594, 210746538, 1557834174, 11620294376, 87357498949, 661194915408, 5034368831334, 38534430714502, 296341243824737, 2288568585083816, 17741278361562738, 138006870242288796, 1076905750814353045
Offset: 0
-
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n+1), k)*binomial(n+(s-1)*k-1, n-k))/(n+1);
A365148
G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^2 )^2.
Original entry on oeis.org
1, 2, 13, 102, 898, 8484, 84061, 861918, 9068950, 97366812, 1062425010, 11747773372, 131350499044, 1482494173128, 16867912278237, 193273940978574, 2228186999313678, 25827663921909228, 300825086742672934, 3519001122784601524, 41325186203051759324
Offset: 0
-
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));
A371614
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2)^2 )^2.
Original entry on oeis.org
1, 2, 5, 26, 138, 814, 5051, 32550, 215792, 1461934, 10077345, 70450980, 498328320, 3559894566, 25646621725, 186122575840, 1359384244220, 9984580141702, 73703387448245, 546492958156148, 4068417329371228, 30397841636794944, 227872480308702892
Offset: 0
-
a(n, r=2, s=2, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Showing 1-4 of 4 results.