A381779
G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^3), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 11, 95, 977, 11028, 132029, 1646428, 21155077, 278127359, 3723466202, 50586670945, 695676081162, 9665426437561, 135464096419620, 1912922793362142, 27190770354633287, 388734441118885467, 5586079818959767743, 80638973170989453862, 1168864771263296930809
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(n+2*k+1, n-k)/(n+4*k+1));
A381785
G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^2), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 7, 45, 335, 2731, 23573, 211741, 1958571, 18529392, 178459000, 1743868792, 17246702932, 172302244669, 1736302280083, 17627794322287, 180133941044517, 1851310247393202, 19123511540724822, 198437973436950204, 2067524004169000212, 21620908821378509071
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(2*k+1, n-k)/(4*k+1));
A381830
G.f. A(x) satisfies A(x) = C(x*A(x)^2) / (1 - x*A(x)), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 10, 69, 558, 4946, 46506, 455587, 4599494, 47517909, 499933964, 5337957532, 57694565830, 630010984557, 6939976239376, 77027050722166, 860564349616694, 9670164031087137, 109221767288604000, 1239281689627682221, 14119315749935075540, 161460732437631678114
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n, n-k)/(n+3*k+1));
Showing 1-3 of 3 results.