This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Concatenation([1,1,1,3],List([4..30],n->3^(n-2)+(Sum([0..n-4],i->(3^i)*(2*(n-i-3))/((n-i-1)*(n-i))*Binomial(2*(n-i-2),n-i-2))))); # Muniru A Asiru, Oct 05 2018
a:=n->`if`(n<=2,1,`if`(n=2,3,3^(n-2)+add((3^i)*(2*(n-i-3))/((n-i-1)*(n-i))*binomial(2*(n-i-2),n-i-2),i=0..n-4))); seq(a(n),n=0..30); # Muniru A Asiru, Oct 05 2018 # Alternative: ogf := x -> 3/2 + (x - sqrt(1 - 4*x))*(2*x - 1)/(6*x - 2): ser := series(ogf(x),x,32): seq(coeff(ser, x, n), n=0..29); # Peter Luschny, Oct 25 2018 # Derivation of the recurrence (requires Maple 2022): FormalPowerSeries:-FindRE(3/2 + (x - sqrt(1 - 4*x))*(2*x - 1)/(6*x - 2),x,a(n)); # Georg Fischer, Oct 21 2022
Flatten[{1, 1, Table[3^(n - 2) + Sum[3^i*2*(n - i - 3)/((n - i - 1)*(n - i)) * Binomial[2*(n - i - 2), n - i - 2], {i, 0, n - 4}], {n, 2, 30}]}] (* Vaclav Kotesovec, Oct 22 2018 *)
a(n) = if (n<=2, 1, if (n==2, 3, 3^(n-2) + sum(i=0, (n-4), (3^i)*(2*(n-i-3))/((n-i-1)*(n-i))*binomial(2*(n-i-2), n-i-2)))); \\ Michel Marcus, Oct 05 2018
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