A109263 A Catalan transform of F(n-1)-0^n.

0, 0, 1, 3, 10, 34, 118, 416, 1485, 5355, 19473, 71313, 262735, 973027, 3619955, 13521307, 50684778, 190597594, 718788034, 2717755820, 10300186824, 39121645886, 148884623768, 567643844338, 2167882951110, 8292331115104

Offset: 0

Author

Paul Barry, Jun 24 2005

Keywords

• easy
• nonn

Comments

A column of A109267.

Define a triangle by T(n,0)=A000045(n) and T(n,k)=sum_{r=k-1..n} T(r,k-1). (The column k=1 is A000071, the column k=2 is A001924 etc). Then T(n,n)=a(n+1). - J. M. Bergot, May 22 2013

Formula

G.f.: x^2c(x)^2/(1-xc(x)-x^2c(x)^2) where c(x) is the g.f. of A000108; a(n)=sum{k=0..n, (k/(2n-k))binomial(2n-k, n-k)(F(k-1)-0^k)}.

Conjecture: n*(n-3)*a(n) +2*(-4*n^2+15*n-10)*a(n-1) +(15*n^2-69*n+80)*a(n-2) +2*(n-2)*(2*n-5)*a(n-3)=0. - R. J. Mathar, Nov 09 2012