A377458
G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^4).
Original entry on oeis.org
1, 1, 1, 4, 7, 29, 61, 256, 596, 2507, 6247, 26197, 68652, 286232, 780508, 3231060, 9102590, 37392935, 108279767, 441342883, 1308552478, 5292781266, 16018989626, 64315663716, 198213843417, 790252270626, 2474924176566, 9802205324516, 31142246753638
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);
A377706
G.f. A(x) satisfies A(x) = 1 + x/A(x)^3 * (1 - A(x) + A(x)^4).
Original entry on oeis.org
1, 1, 0, 3, -6, 28, -105, 444, -1897, 8338, -37305, 169471, -779537, 3623500, -16993990, 80316081, -382136133, 1828896726, -8798796709, 42528048930, -206413678447, 1005623593109, -4916026689088, 24106987842416, -118551374861525, 584526569727010, -2888995759466360
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(n-4*k, n-k-1))/n);
A378919
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)).
Original entry on oeis.org
1, 1, 5, 39, 355, 3532, 37206, 407861, 4604493, 53169811, 625067441, 7456004083, 90015754691, 1097834790182, 13505674728174, 167395320811562, 2088350145491232, 26203315734195937, 330460721192844017, 4186559092558049570, 53255890990455126082, 679954025388880445771
Offset: 0
-
a(n, r=1, s=-1, t=6, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A378958
G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 - A(x) + A(x)^4).
Original entry on oeis.org
1, 1, 2, 8, 32, 145, 681, 3337, 16773, 86181, 450268, 2385544, 12784861, 69189509, 377576512, 2075423744, 11480230037, 63857579629, 356962271136, 2004255583560, 11298268724556, 63919517790933, 362806671879955, 2065443363987045, 11790688867079872, 67477283970889867
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(3*n-4*k, n-k-1))/n);
Showing 1-4 of 4 results.