0,3

Also main diagonal of array : m(i,1)=1, i>=1; m(1,j)=2, j>1; m(i,j)=m(i,j-1)+m(i-1,j-1)+m(i-1,j): 1 2 2 2 ... / 1 4 8 12 ... / 1 6 18 38 ... / 1 8 32 88 ... / - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2002

a(n) is also the number of order-preserving partial transformations (of an n-element chain) of waist n (waist(alpha) = max(Im(alpha))). [From A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008]

Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278, (2004), 342-359. [From A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008]

Munarini, Emanuele, Combinatorial properties of the antichains of a garland. Integers, 9 (2009), 353-374.

Coefficient of x^(n-1) in expansion of ((1+x)/(1-x))^n, n>0. a(n) = Sum_{k=1..n} binomial(n, k)*binomial(n+k-2, k-1), n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 31 2004

(n-1)*(n-2)*a(n) = 3*(2*n-3)*(n-2)*a(n-1)-(n-1)*(n-3)*a(n-2), n>2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 16 2004

a(n+1)=Jacobi_P(n, 1, -1, 3); a(n+1)=sum{k=0..n, C(n+1, k)C(n-1, n-k)2^k}; - Paul Barry (pbarry(AT)wit.ie), Jan 23 2006

a(n)= n*A006318(n-1) [From A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008]

Cf. A002003, A050151.

A006318 [From A. Umar (aumarh(AT)squ.edu.om), Aug 25 2008]

Sequence in context: A164045 A130524 A083325 this_sequence A083879 A081671 A006629

Adjacent sequences: A050143 A050144 A050145 this_sequence A050147 A050148 A050149

nonn

Clark Kimberling (ck6(AT)evansville.edu)