A364740
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^5).
Original entry on oeis.org
1, 1, 3, 15, 91, 607, 4298, 31720, 241321, 1879097, 14903013, 119965086, 977623639, 8049579047, 66864689674, 559650696185, 4715304229460, 39960204165865, 340395043021399, 2912963919210012, 25031055321749916, 215894227588453950, 1868403327770467149
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(2*n+3*k, n-1-k))/n);
A364764
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 1, -2, -14, -27, 70, 625, 1457, -3541, -37403, -98547, 207098, 2564079, 7448923, -12940485, -190014459, -600991549, 827159379, 14802832468, 50584687754, -52159768068, -1193457862093, -4384199208207, 3090291576246, 98618925147291, 388126462227091
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+2*k, n-1-k))/n);
A365247
G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)^4).
Original entry on oeis.org
1, 1, 2, 5, 15, 50, 177, 650, 2449, 9412, 36761, 145518, 582556, 2354557, 9594898, 39378259, 162619316, 675258452, 2817643240, 11808576745, 49683880754, 209786559004, 888676860191, 3775654643360, 16084818268474, 68694452578325, 294053067958011
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-2*k+1, n-3*k)/(2*n-2*k+1));
A364723
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^4).
Original entry on oeis.org
1, 1, 2, 8, 38, 196, 1073, 6120, 35968, 216304, 1324676, 8232981, 51796538, 329229344, 2111031444, 13638557196, 88695018723, 580153216512, 3814285704000, 25192499164320, 167075960048996, 1112162062296061, 7428213584196010, 49766086788057256
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(n+3*k, n-1-k))/n);
A365246
G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^4).
Original entry on oeis.org
1, 1, 2, 6, 22, 88, 370, 1613, 7230, 33117, 154330, 729369, 3487470, 16840346, 82007012, 402269702, 1985867630, 9858739759, 49187798158, 246506563980, 1240337033398, 6263601365616, 31734939452116, 161270637750264, 821802841072422, 4198348868249768
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(2*n+1, n-2*k))/(2*n+1);
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));
Showing 1-6 of 6 results.