A026033 a(n) = C(4*n,n) - C(4*n,n-4).

1, 4, 28, 220, 1819, 15484, 134320, 1180764, 10482340, 93766288, 843822148, 7631018564, 69291185474, 631334484200, 5769124912320, 52851389067420, 485242722376524, 4463782855666480, 41133265444555120, 379620280119739120, 3508357921081665795, 32463749094788984220

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Formula

a(n) = T(4*n, n), where T is defined in A026022.

G.f.: (g-2)*(2-2*g+g^2)*g^2/(3*g-4) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011

a(n) ~ 5 * 2^(8*n+9/2) / (3^(3*n+9/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 18 2025

Mathematica

A026033[n_] := Binomial[4*n, n] - Binomial[4*n, n - 4];
Array[A026033, 25, 0] (* Paolo Xausa, Sep 11 2025 *)

Crossrefs

Cf. A002293, A026022.

Sequence in context: A182432 A026020 A243116 * A005810 A387990 A371755

Adjacent sequences: A026030 A026031 A026032 * A026034 A026035 A026036

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Ralf Stephan, Jan 09 2005

More terms from Jason Yuen, Sep 11 2025

Status

approved