A359176 a(n) = binomial(2*n-2,n-1) - n.

0, 0, 3, 16, 65, 246, 917, 3424, 12861, 48610, 184745, 705420, 2704143, 10400586, 40116585, 155117504, 601080373, 2333606202, 9075135281, 35345263780, 137846528799, 538257874418, 2104098963697, 8233430727576, 32247603683075, 126410606437726, 495918532948077

Offset

1,3

Comments

a(n) is the number of ways to place n-1 indistinguishable balls into n distinguishable boxes with not all balls placed in one box.

Links

Stefano Spezia, Table of n, a(n) for n = 1..1600

Formula

a(n) = A000984(n-1) - n.

G.f.: x*(1/sqrt(1 - 4*x) - 1/(1 - x)^2). - Stefano Spezia, Dec 28 2022

D-finite with recurrence: (-n+1)*a(n) +(5*n-8)*a(n-1) +2*(-2*n+5)*a(n-2) +6*(n-2)=0. - R. J. Mathar, Jan 25 2023

From Stefano Spezia, Apr 25 2023:

E.g.f.: x*exp(x)*(exp(x)*(BesselI(0,2*x) - BesselI(1,2*x)) - 1).

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

Mathematica

a[n_] := Binomial[2*n - 2, n - 1] - n; Array[a, 30] (* Amiram Eldar, Dec 30 2022 *)

Crossrefs

Cf. A000984.

Sequence in context: A037451 A247363 A007143 * A062960 A293579 A044046

Adjacent sequences: A359173 A359174 A359175 * A359177 A359178 A359179

Keyword

nonn

Author

Enrique Navarrete, Dec 28 2022

Status

approved