A383525 -id:A383525 - cp's OEIS frontend

A383539 a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k)^2 * binomial(n-2*k,k).

1, 1, 1, 5, 19, 49, 137, 481, 1645, 5259, 17309, 59477, 203931, 693865, 2384149, 8277773, 28797631, 100312525, 350891175, 1232122535, 4335809699, 15287669469, 54029225569, 191351513905, 678850904981, 2412164275651, 8584573648693, 30595269827149

Offset: 0

Seiichi Manyama, Apr 29 2025

nonn

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x^2*y^2*z^3).

Robert Israel, Table of n, a(n) for n = 0..1758

Cf. A383525, A383537.

Cf. A098479.

f:= proc(n) local k; add(binomial(n-k,k)^2 * binomial(n-2*k,k),k=0..n/3) end proc:
map(f, [$0..30]); # Robert Israel, May 29 2025

a(n) = sum(k=0, n\3, binomial(n-k, k)^2*binomial(n-2*k, k));

A383526 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k,k)^2.

Original entry on oeis.org

1, 1, 1, 4, 17, 46, 112, 365, 1297, 4126, 12686, 41647, 141440, 470887, 1553021, 5205769, 17665105, 59858038, 202599814, 689183087, 2355887902, 8065291637, 27637715887, 94924591313, 326810899744, 1126888746871, 3890420726167, 13450563963085, 46571447873597

Offset: 0

Seiichi Manyama, Apr 29 2025

nonn

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x*y^3*z^3).

Cf. A000172, A248658, A383525.

a(n) = sum(k=0, n\3, binomial(n, k)*binomial(n-2*k, k)^2);

cp's OEIS Frontend

A383539 a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k)^2 * binomial(n-2*k,k).

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