A379331
G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x*A(x)^3) * (1 - 2*x*A(x)) ).
Original entry on oeis.org
1, 2, 12, 100, 976, 10432, 118216, 1395200, 16965664, 211078656, 2674095616, 34378044416, 447359023072, 5881178595328, 77992591652992, 1042089880305664, 14015275654390272, 189583355671740416, 2577607282441795840, 35205701425533550592, 482822120552883164160
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k+1/2, k)*binomial(3*n/2-1/2, n-k)/(n+4*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));
A379382
G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^2) ).
Original entry on oeis.org
1, 2, 8, 48, 336, 2560, 20608, 172416, 1484288, 13062144, 116977664, 1062600704, 9767067648, 90673700864, 848971661312, 8007542571008, 76014137180160, 725681289822208, 6962697126019072, 67105309925048320, 649362348326256640, 6306663216709632000
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+3*k/2-1/2, k)*binomial(n/2+k/2+1/2, n-k)/(n+k+1));
Showing 1-3 of 3 results.