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URL: https://oeis.org/A390239

⇱ A390239 - OEIS

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A390239
a(n) = Sum_{k=0..n} binomial(3*n-2*k+2,n-k).
7
1, 6, 35, 209, 1275, 7904, 49589, 313974, 2002220, 12841751, 82752021, 535345045, 3474775708, 22617821463, 147584362683, 965075220369, 6322701872061, 41492819788931, 272705878101320, 1794740376416679, 11826005670886204, 78010902726869575, 515123218691304651
OFFSET
0,2
LINKS
FORMULA
G.f.: g^2/((1-3*x*g^2) * (1-x*g)) where g = 1+x*g^3 is the g.f. of A001764.
From Vaclav Kotesovec, Nov 09 2025: (Start)
a(n) = Sum_{k=0..n} binomial(n+2*k+2, k).
a(n) ~ 3^(3*n + 9/2) / (7*sqrt(Pi*n) * 2^(2*n+3)). (End)
From Seiichi Manyama, Nov 10 2025: (Start)
a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n+k+4,n-k).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-k+3,n-2*k). (End)
MATHEMATICA
a[n_]:=Sum[Binomial[3*n-2*k+2, n-k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Vincenzo Librandi, Oct 31 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(3*n-2*k+2, n-k));
(Magma) [&+[Binomial(3*n-2*k+2, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Oct 31 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 30 2025
STATUS
approved