cp's OEIS Frontend

A060063 Triangle of coefficients of certain polynomials used for G.f.s of columns of triangle A060058.

%I A060063 #14 Aug 28 2019 16:44:46
%S A060063 1,1,1,5,26,9,61,775,1179,225,1385,32516,114318,87156,11025,50521,
%T A060063 1894429,11982834,20371266,9652725,893025,2702765,148008446,
%U A060063 1472351967,4417978068,4546174779,1502513550
%N A060063 Triangle of coefficients of certain polynomials used for G.f.s of columns of triangle A060058.
%C A060063 The row polynomials p(n,x) (rising powers of x) appear as numerators of the column g.f.s of triangle A060058.
%C A060063 First column (m=0) gives A000364 (Euler numbers). See A091742, A091743, A091744 for columns m=1..3.
%C A060063 The main diagonal gives A001818. The row sums give A052502. The alternating row sums give A091745.
%H A060063 W. Lang, <a href="/A060063/a060063.txt">First 8 rows</a>.
%F A060063 The row polynomials p(n, x) := Sum_{m=0..n} a(n, m)*x^m satisfy the differential equation: p(n, x) = x*((1-x)^2)*(d^2/dx^2)p(n-1, x) + (1+6*(n-1)*x+(5-6*n)*x^2)*(d/dx)p(n-1, x) + (3*n-2)*(1+(3*n-2)*x)*p(n-1, x), n >= 1, with input p(0, x)=1. - _Wolfdieter Lang_, Feb 13 2004
%e A060063 Triangle begins:
%e A060063   {1};
%e A060063   {1,1};
%e A060063   {5,26,9};     <-- p(2,n)=5+26*x+9*x^2.
%e A060063   {61,775,1179,225};
%e A060063   ...
%K A060063 nonn,easy,tabl
%O A060063 0,4
%A A060063 _Wolfdieter Lang_, Mar 16 2001