A289719 a(n) = (n/2)*binomial(2*n, n) + 1.

1, 2, 7, 31, 141, 631, 2773, 12013, 51481, 218791, 923781, 3879877, 16224937, 67603901, 280816201, 1163381401, 4808643121, 19835652871, 81676217701, 335780006101, 1378465288201, 5651707681621, 23145088600921, 94684453367401, 386971244197201, 1580132580471901

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, corollary 37, tables 4.1 and 4.2

Formula

a(n) = 1 + A002457(n-1).

Maple

seq(1+n/2*binomial(2*n, n), n=0..20) ;

Mathematica

Table[(n/2) Binomial[2 n, n] + 1, {n, 0, 20}] (* Michael De Vlieger, Sep 05 2017 *)

Prog

(GAP)
A289719:=List([0..10^2], n->(n/2)*Binomial(2*n, n)+1); # Muniru A Asiru, Sep 03 2017
(PARI) a(n) = {n*binomial(2*n, n)/2 + 1} \\ Andrew Howroyd, Apr 26 2020

Crossrefs

Cf. A002457, A289720.

Sequence in context: A343532 A034698 A115605 * A114198 A349769 A358963

Adjacent sequences: A289716 A289717 A289718 * A289720 A289721 A289722

Keyword

nonn,easy

Author

R. J. Mathar, Sep 02 2017

Extensions

Terms a(21) and beyond from Andrew Howroyd, Apr 26 2020

Status

approved