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));
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));
A378890
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 + x*A(x)^(2/3)) )^3.
Original entry on oeis.org
1, 3, 15, 97, 711, 5613, 46552, 399918, 3527553, 31761600, 290721387, 2697131541, 25304974597, 239684681523, 2288849098119, 22012319667437, 213011739042714, 2072597720747352, 20264567643461700, 198998140737895692, 1961831436443431818, 19409477239837165874
Offset: 0
-
a(n, r=3, s=-1, t=5, 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));
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 1-4 of 4 results.