A037958 a(n) = binomial(n, floor((n-8)/2)).

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 11, 66, 78, 364, 455, 1820, 2380, 8568, 11628, 38760, 54264, 170544, 245157, 735471, 1081575, 3124550, 4686825, 13123110, 20030010, 54627300, 84672315, 225792840, 354817320, 927983760, 1476337800, 3796297200, 6107086800, 15471286560

Offset

0,11

Links

Robert Israel, Table of n, a(n) for n = 0..3324

Formula

Conjecture: -(n+9)*(n-8)*a(n) +2*(n)*a(n-1) + 4*n*(n-1)*a(n-2) = 0. - R. J. Mathar, Jul 26 2015, verified by Robert Israel, Jun 28 2018

From Robert Israel, Jun 28 2018: (Start)

E.g.f.: I_8(2*x)+I_9(2*x), where I_k is the modified Bessel function of the first kind and order k.

G.f.: 256*x^8/((1+sqrt(1-4*x^2))^8*sqrt(1-4*x^2)) + 512*x^9/((1+sqrt(1-4*x^2))^9*sqrt(1-4*x^2)). (End)

a(n) ~ 2^(n+1/2) / sqrt(Pi*n). - Amiram Eldar, Sep 22 2025

Maple

seq(binomial(n, floor((n-8)/2)), n=0..50); # Robert Israel, Jun 28 2018

Mathematica

Table[Binomial[n, Floor[(n-8)/2]], {n, 0, 40}] (* Harvey P. Dale, Jun 11 2013 *)

Prog

(GAP) List([0..40], n->Binomial(n, Int((n-8)/2))); # Muniru A Asiru, Jun 29 2018

Crossrefs

Sequence in context: A387357 A335553 A122602 * A041214 A228381 A262229

Adjacent sequences: A037955 A037956 A037957 * A037959 A037960 A037961

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved