A030054 a(n) = binomial(2n+1,n-4).

1, 11, 78, 455, 2380, 11628, 54264, 245157, 1081575, 4686825, 20030010, 84672315, 354817320, 1476337800, 6107086800, 25140840660, 103077446706, 421171648758, 1715884494940, 6973199770790, 28277527346376, 114456658306760, 462525733568080, 1866442158555975

Offset

4,2

Links

Robert Israel, Table of n, a(n) for n = 4..1661

Milan Janjic, Two Enumerative Functions.

Formula

G.f.: x^4*512/((1-sqrt(1-4*x))^9*sqrt(1-4*x))+(-1/x^5+7/x^4-15/x^3+10/x^2-1/x). - Vladimir Kruchinin, Aug 11 2015

From Robert Israel, Jun 11 2019: (Start)

(54 + 36*n)*a(n) + (-438 - 129*n)*a(n + 1) + (714 + 138*n)*a(n + 2) + (-432 - 63*n)*a(n + 3) + (110 + 13*n)*a(n + 4) + (-10 - n)*a(n + 5) = 0.

a(n) ~ 2^(2*n+1)/sqrt(n*Pi). (End)

From Amiram Eldar, Jan 24 2022: (Start)

Sum_{n>=4} 1/a(n) = 317/210 - 2*Pi/(9*sqrt(3)).

Sum_{n>=4} (-1)^n/a(n) = 2908*log(phi)/(5*sqrt(5)) - 8697/70, where phi is the golden ratio (A001622). (End)

G.f.: 2F1([11/2,5],[10],4*x). - Karol A. Penson, Apr 24 2024

Maple

seq(binomial(2*n+1, n-4), n=4..50); # Robert Israel, Jun 11 2019

Mathematica

Table[Binomial[2n+1, n-4], {n, 4, 40}]  (* Harvey P. Dale, Mar 31 2011 *)

Prog

(PARI) vector(30, n, m=n+4; binomial(2*m+1, m-4)) \\ Michel Marcus, Aug 11 2015

Crossrefs

Diagonal 10 of triangle A100257.

Fifth unsigned column (s=4) of A113187. - Wolfdieter Lang, Oct 19 2012

Cf. A001622.

Sequence in context: A206529 A118936 A041224 * A225896 A239437 A140542

Adjacent sequences: A030051 A030052 A030053 * A030055 A030056 A030057

Keyword

nonn

Author

N. J. A. Sloane

Status

approved