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URL: https://oeis.org/A389286

⇱ A389286 - OEIS

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A389286
G.f. A(x) satisfies A(x) = 1 + x/(1-x^3)^2 * A(x)^3.
3
1, 1, 3, 12, 57, 285, 1500, 8195, 46023, 264063, 1541227, 9121923, 54619314, 330265437, 2013832533, 12369068985, 76455159257, 475232409786, 2968677006729, 18627255774187, 117346391111751, 741923837211168, 4706241730137593, 29942623860897282, 191028099206837802
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k-1,k) * A001764(n-3*k).
MATHEMATICA
Table[Sum[Binomial[2*n-5*k-1, k]*Binomial[3*(n-3*k), n-3*k]/(2*(n-3*k)+1), {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 15 2025 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k-1, k)*binomial(3*(n-3*k), n-3*k)/(2*(n-3*k)+1));
(Magma) [&+[Binomial(2*n-5*k-1, k)*Binomial(3*(n-3*k), n-3*k)/(2*(n-3*k)+1): k in [0..Floor(n/3)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 15 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 26 2025
STATUS
approved