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

0,4

Comments

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

Links

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

Maple

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

Prog

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

Crossrefs

Cf. A383525, A383537.

Cf. A098479.

Sequence in context: A328191 A100104 A015650 * A200764 A285987 A055365

Adjacent sequences: A383536 A383537 A383538 * A383540 A383541 A383542

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2025

Status

approved