A371612
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2) )^2.
Original entry on oeis.org
1, 2, 3, 12, 49, 218, 1037, 5106, 25909, 134410, 709691, 3801498, 20606654, 112828202, 623087675, 3466539248, 19411070496, 109313442562, 618713495451, 3517737628368, 20081523836403, 115058714898196, 661432784830204, 3813891082337178, 22052422636145522
Offset: 0
-
a(n, r=2, s=1, 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));
A378411
G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^(3/2)) )^2.
Original entry on oeis.org
1, 2, 3, 8, 19, 50, 137, 380, 1088, 3152, 9270, 27576, 82794, 250700, 764454, 2345688, 7237318, 22438988, 69876356, 218456216, 685400835, 2157396738, 6810801959, 21559694364, 68417766207, 217617573110, 693655532081, 2215401956720, 7088605614314, 22720370822508
Offset: 0
-
a(n, r=2, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A378787
G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^2)^3 )^2.
Original entry on oeis.org
1, 2, 7, 36, 197, 1184, 7425, 48308, 322521, 2198064, 15227850, 106924154, 759245463, 5442675080, 39335090088, 286296369000, 2096706604597, 15439417451928, 114243931954962, 849030345258990, 6334510149389409, 47428709540589036, 356261301882333885
Offset: 0
-
a(n, r=2, s=3, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Showing 1-3 of 3 results.