A389284 G.f. A(x) satisfies A(x) = 1 + x/(1-x^2)^2 * A(x)^3.

1, 1, 3, 14, 67, 348, 1898, 10738, 62439, 370895, 2241012, 13730328, 85103286, 532673423, 3362122902, 21375465814, 136763670651, 879940122276, 5689726482333, 36953647770610, 240966724401636, 1576974511448612, 10354207594395232, 68188193149899870

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1,k) * A001764(n-2*k).

Mathematica

Table[Sum[Binomial[2*n-3*k-1, k]*Binomial[3*(n-2*k), n-2*k]/(2*(n-2*k)+1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 14 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(2*n-3*k-1, k)*binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1));
(Magma) [&+[Binomial(2*n-3*k-1, k)*Binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1): k in [0..Floor(n/2)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 14 2025

Crossrefs

Cf. A366176, A389286.

Cf. A001764, A387063.

Sequence in context: A002320 A151323 A385065 * A354503 A181662 A241478

Adjacent sequences: A389281 A389282 A389283 * A389285 A389286 A389287

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 26 2025

Status

approved