A379330
G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x*A(x)^2) * (1 - 2*x*A(x)) ).
Original entry on oeis.org
1, 2, 10, 66, 500, 4112, 35702, 322114, 2990450, 28382486, 274151074, 2686200302, 26634199776, 266738477892, 2694291026378, 27416542767134, 280790643343716, 2892142875601024, 29939599990333394, 311334925950172590, 3250627732373638716, 34063930480000774400, 358149513590192454578
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+3*k/2+1/2, k)*binomial(3*n/2-k/2-1/2, n-k)/(n+3*k+1));
A379329
G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x) * (1 - 2*x*A(x)) ).
Original entry on oeis.org
1, 2, 6, 22, 92, 420, 2034, 10262, 53330, 283410, 1532698, 8406698, 46650072, 261416000, 1477208374, 8407900890, 48158339716, 277375020772, 1605477915982, 9333727605762, 54478721494436, 319120526072380, 1875410643820166, 11054224586789010, 65334486288626586, 387118590382759994
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+k/2+1/2, k)*binomial(3*n/2-3*k/2-1/2, n-k)/(n+k+1));
A379383
G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^3) ).
Original entry on oeis.org
1, 2, 10, 80, 750, 7680, 83252, 939008, 10905942, 129548288, 1566565452, 19220267008, 238662840780, 2993651974144, 37876206019560, 482802294325248, 6194365014836582, 79930063134392320, 1036640587694252380, 13505632613590630400, 176673045664669396132, 2319654465118014537728
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k-1/2, k)*binomial(n/2+k+1/2, n-k)/(n+2*k+1));
Showing 1-3 of 3 results.