A371613
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3) )^2.
Original entry on oeis.org
1, 2, 3, 16, 83, 460, 2767, 17210, 110308, 723624, 4832363, 32747106, 224619408, 1556484636, 10879744696, 76621739626, 543159825499, 3872610857558, 27752175177823, 199787917082084, 1444171829169939, 10477887409768628, 76275565075016394
Offset: 0
-
a(n, r=2, s=1, t=0, u=6) = 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));
A371607
G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^2) )^2.
Original entry on oeis.org
1, 2, 3, 10, 29, 92, 314, 1078, 3830, 13844, 50746, 188554, 707667, 2679960, 10227940, 39294772, 151859858, 589943516, 2302462140, 9023681820, 35498194465, 140122652960, 554827907272, 2203135245820, 8771143399104, 35003747271444, 140002994665366
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(s*k, n-k)/(t*k+u*(n-k)+r));
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));
A378731
G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)^(4/3)) )^3.
Original entry on oeis.org
1, 3, 6, 22, 93, 417, 1993, 9864, 50217, 261239, 1382448, 7418877, 40278175, 220830513, 1220930337, 6799458685, 38107621704, 214771481163, 1216457185122, 6920603372448, 39529745832681, 226605757331904, 1303291125124071, 7518151040142000, 43488151271999326
Offset: 0
-
a(n, r=3, 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));
A378732
G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)) )^4.
Original entry on oeis.org
1, 4, 10, 36, 155, 704, 3384, 16844, 86097, 449344, 2384170, 12822556, 69743953, 382982940, 2120323014, 11822279232, 66327376437, 374162700460, 2120999728610, 12075668658000, 69021358842795, 395909382981572, 2278286453089574, 13149207655326372, 76096242994616990
Offset: 0
-
a(n, r=4, 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));
Showing 1-5 of 5 results.