A364864
G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 2, 4, 6, -1, -58, -304, -1090, -2876, -4216, 9244, 106746, 529962, 1874628, 4669760, 4309742, -35179252, -277928680, -1269921008, -4214431912, -9197175241, 30113526, 128659598896, 822227670866, 3453484223084, 10519017940952, 18490932535144
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
A378891
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^2/(1 + x*A(x)) )^3.
Original entry on oeis.org
1, 3, 18, 142, 1278, 12429, 127223, 1350456, 14729628, 164079982, 1858781652, 21348787587, 248021665720, 2909439099543, 34413536180688, 409984974779725, 4915119769384221, 59252402698999209, 717819918438472134, 8734481867945979183, 106703642464149880248
Offset: 0
-
a(n, r=3, s=-1, t=6, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A378920
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 5, 38, 339, 3308, 34191, 367844, 4076112, 46204209, 533239820, 6244542391, 74016115926, 886276231388, 10704869669941, 130271156244371, 1595708949486866, 19658780721376791, 243429900033986385, 3028086095940468087, 37821457123957529163, 474145963420441744445
Offset: 0
-
a(n, r=1, s=-1, t=6, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
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));
A377705
G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^3).
Original entry on oeis.org
1, 1, 0, 2, -3, 12, -35, 121, -413, 1464, -5265, 19249, -71236, 266443, -1005511, 3824055, -14641264, 56389272, -218315173, 849170605, -3316817080, 13004273475, -51160638706, 201901154910, -799059730844, 3170706566751, -12611882813645, 50277271079611
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(n-3*k, n-k-1))/n);
Showing 1-5 of 5 results.