A365118
G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^2.
Original entry on oeis.org
1, 2, 3, 8, 23, 72, 237, 808, 2830, 10118, 36779, 135510, 504935, 1899494, 7204238, 27517766, 105761937, 408715018, 1587169591, 6190357852, 24238696551, 95244997612, 375469654543, 1484519159122, 5885302251250, 23389997790804, 93172394487012
Offset: 0
-
a(n, s=1, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A378882
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)/(1 - x*A(x)^(5/3)) )^3.
Original entry on oeis.org
1, 3, 15, 97, 717, 5736, 48340, 422688, 3799080, 34881159, 325750143, 3084634305, 29548452297, 285825135183, 2787990695931, 27391816756281, 270828413410413, 2692692976016352, 26904718314949776, 270017389769189136, 2720718671661444780, 27513054621821846074
Offset: 0
-
a(n, r=3, s=1, t=3, u=5) = 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));
A378828
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(2/3)/(1 - x*A(x)^(4/3)) )^3.
Original entry on oeis.org
1, 3, 12, 61, 354, 2220, 14649, 100218, 704373, 5055383, 36895221, 272975652, 2042782905, 15434838759, 117588475377, 902259691317, 6966487019220, 54086849181609, 421986564474946, 3306818224272945, 26015737668878523, 205405810986995869, 1627042895593132485
Offset: 0
-
a(n, r=3, s=1, t=2, 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));
A378858
G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(3/4)) )^4.
Original entry on oeis.org
1, 4, 10, 32, 119, 468, 1934, 8256, 36135, 161276, 731158, 3357748, 15587004, 73021200, 344786056, 1639145180, 7839483967, 37692820908, 182087119582, 883358016328, 4301799946048, 21021519618724, 103049029114618, 506608410994868, 2497162797380145, 12338908560964968
Offset: 0
-
a(n, r=4, s=1, t=0, u=3) = 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.