A371523
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1-x))^2.
Original entry on oeis.org
1, 2, 15, 142, 1533, 17924, 220936, 2827218, 37202580, 500228562, 6842899886, 94931338876, 1332438761910, 18887047322030, 269986427261981, 3887654399820062, 56337997080499605, 821021578186212094, 12024687038651388155, 176900548019426869808, 2612917215947948178941
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+1, k)/(5*k+2));
A371517
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^4.
Original entry on oeis.org
1, 4, 26, 188, 1459, 11892, 100444, 871528, 7722557, 69590628, 635807180, 5876094308, 54836925779, 516029817620, 4891147100886, 46653935716492, 447490869463145, 4313492172957396, 41763413498670702, 405968522259130636, 3960526930400038404
Offset: 0
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+3, k)/(3*k+4));
A371583
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x) )^2.
Original entry on oeis.org
1, 2, 13, 104, 940, 9166, 94044, 1000602, 10939780, 122161128, 1387361151, 15974899766, 186069556707, 2188416960148, 25953579753464, 310022550197360, 3726709235290628, 45047517497268968, 547217895030263028, 6676784544374859088, 81789906534091716353
Offset: 0
-
a(n, r=2, s=1, t=5, u=0) = 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));
A371545
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^2.
Original entry on oeis.org
1, 2, 7, 36, 209, 1312, 8663, 59298, 416961, 2993790, 21857208, 161768154, 1210949944, 9152366596, 69745701746, 535304423948, 4134240993874, 32105769989714, 250551371644825, 1963871015580984, 15454014753626079, 122044659649929546, 966951068210379441
Offset: 0
-
a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(4*k+2, k)/(4*k+2));
Showing 1-4 of 4 results.