A390542 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+2*k+1,k).

1, 3, 17, 97, 580, 3549, 22070, 138839, 881047, 5629040, 36160422, 233329967, 1511210765, 9818610764, 63966280085, 417707613785, 2733299156728, 17918056518711, 117651211075754, 773624422079360, 5093656865657644, 33576955192412844, 221573948545741693

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: g/((1-3*x*g^2) * (1+x*g)) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[n+2*k+1, k], {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 11 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+2*k+1, k));
(Magma) [&+[(-1)^(n-k)*Binomial(n+2*k+1, k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 11 2025

Crossrefs

Cf. A005809, A371785, A390541, A390543, A390544, A390545.

Cf. A001764.

Sequence in context: A302871 A010913 A142988 * A356267 A056660 A155610

Adjacent sequences: A390539 A390540 A390541 * A390543 A390544 A390545

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved