A367239
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^2)^3.
Original entry on oeis.org
1, 1, 4, 19, 104, 615, 3829, 24728, 164122, 1112641, 7671781, 53634389, 379305155, 2708686547, 19505022538, 141470864166, 1032587621470, 7578835132264, 55901583657799, 414157062713599, 3080581445049863, 22996511364853472, 172230640045929990
Offset: 0
-
a(n, s=3, t=1, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A367241
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^2)^3.
Original entry on oeis.org
1, 1, 6, 42, 335, 2886, 26166, 246028, 2377161, 23459250, 235452723, 2395998060, 24663705924, 256358715585, 2686893609015, 28364934291912, 301334854075058, 3219067773992448, 34558507062732315, 372646872976093760, 4034272938342360147
Offset: 0
-
a(n, s=3, t=3, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A367281
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 5, 32, 237, 1906, 16179, 142665, 1294115, 11998349, 113194205, 1083131419, 10486939473, 102548233212, 1011333385507, 10047289999536, 100458873883179, 1010138430187185, 10208244014494347, 103625607305637693, 1056166710786300973
Offset: 0
-
a(n, s=3, t=2, u=3) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A367285
G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^2)^3.
Original entry on oeis.org
1, 1, 5, 26, 159, 1042, 7185, 51340, 376806, 2823734, 21516113, 166196703, 1298413089, 10241803340, 81454834164, 652465062453, 5259084437170, 42624217133130, 347160390473763, 2839928983316595, 23323730673818467, 192237734035157372, 1589602164422747636
Offset: 0
-
a(n, s=3, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));
Showing 1-4 of 4 results.