A387550 a(n) = (1/2) * Sum_{k=0..n} 2^k * binomial(2*k+2,2*n-2*k+1).

1, 4, 16, 72, 316, 1376, 6016, 26304, 114960, 502464, 2196224, 9599360, 41957312, 183389184, 801566720, 3503527936, 15313395968, 66932560896, 292552200192, 1278701856768, 5589014330368, 24428744679424, 106774384771072, 466694846300160, 2039853285314560

Offset: 0

Author

Seiichi Manyama, Sep 01 2025

Keywords

• nonn
• easy
• new

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,8,-4).

Crossrefs

Cf. A375276.

Programs

Magma

[&+[2^k * Binomial(2*k+2, 2*n-2*k+1)/2: k in [0..n]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Mathematica

Table[Sum[2^k*Binomial[2*k+2,2*n-2*k+1]/2,{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Sep 02 2025 *)

PARI

a(n) = sum(k=0, n, 2^k*binomial(2*k+2, 2*n-2*k+1))/2;

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A375276.

G.f.: 1/((1-2*x-2*x^2)^2 - 16*x^3).

a(n) = 4*a(n-1) + 8*a(n-3) - 4*a(n-4).