A289720 a(n) = 1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2.

1, 2, 7, 34, 193, 1036, 5059, 23094, 101329, 434908, 1843411, 7753582, 32441017, 135195464, 561615643, 2326740526, 9617257185, 39671268460, 163352388259, 671559953358, 2756930503801, 11303415274600, 46290177094635, 189368906606254, 773942488241473, 3160265160763176

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 42, tables 4.3 and 4.4

Formula

(n-1)*(69642*n - 248963)*a(n) + (-358060*n^2 + 1078397*n - 66480)*a(n-1) + 3*(56652*n^2 + 710433*n - 1732769)*a(n-2) + (749910*n^2 - 7663147*n + 14398378)*a(n-3) - 2*(157862*n - 346287)*(2*n - 7)*a(n-4) = 0.

Maple

seq(n*binomial(2*n, n)+1-n^2*(n^2-2*n+3)/2, n=0..20) ;

Prog

(GAP)
A289720:=List([0..10^3], n->1+n*Binomial(2*n, n)-(n^2*(n^2-2*n+3))/2); # Muniru A Asiru, Sep 03 2017
(PARI) a(n) = {1 + n*binomial(2*n, n) - n^2*(n^2 - 2*n + 3)/2} \\ Andrew Howroyd, Apr 26 2020

Crossrefs

Cf. A289719.

Sequence in context: A273030 A020054 A206240 * A190631 A326560 A199475

Adjacent sequences: A289717 A289718 A289719 * A289721 A289722 A289723

Keyword

nonn,easy

Author

R. J. Mathar, Sep 02 2017

Extensions

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

Status

approved