A109263 - OEIS

%I #12 May 26 2013 10:39:49

%S 0,0,1,3,10,34,118,416,1485,5355,19473,71313,262735,973027,3619955,

%T 13521307,50684778,190597594,718788034,2717755820,10300186824,

%U 39121645886,148884623768,567643844338,2167882951110,8292331115104

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

%C A column of A109267.

%C 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

%F 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)}.

%F 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

%K easy,nonn

%O 0,4

%A _Paul Barry_, Jun 24 2005