A364758
G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)).
Original entry on oeis.org
1, 1, 3, 14, 76, 450, 2818, 18352, 123028, 843345, 5884227, 41650479, 298352365, 2158751879, 15754446893, 115830820439, 857147952469, 6379136387303, 47715901304501, 358529599468636, 2704884469806606, 20481615947325089, 155605509972859999, 1185779099027494848
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(4*n-3*k, n-1-k))/n);
-
a(n, r=1, s=-1, t=4, 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)); \\ Seiichi Manyama, Dec 11 2024
A365225
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 4, 24, 169, 1301, 10605, 89963, 785943, 7023148, 63892489, 589771350, 5509967214, 52001860377, 495048989686, 4748144843341, 45838627944500, 445072967642096, 4343508043479012, 42581707009501604, 419158119684986781, 4141270208611084284
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(2*n+3*k+1, k)*binomial(n-1, n-k)/(2*n+3*k+1));
A365226
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^6).
Original entry on oeis.org
1, 1, 4, 20, 107, 577, 3010, 14429, 56640, 98020, -1297568, -21901213, -232421636, -2081040375, -16862259358, -126674303915, -887771735205, -5768588276072, -33971373570320, -170393703586467, -576946353425125, 1101490168511323, 47657979846612682
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n-k+1, k)*binomial(n-1, n-k)/(6*n-k+1));
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 1-7 of 7 results.