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

1, 1, 1, 5, 26, 9, 61, 775, 1179, 225, 1385, 32516, 114318, 87156, 11025, 50521, 1894429, 11982834, 20371266, 9652725, 893025, 2702765, 148008446, 1472351967, 4417978068, 4546174779, 1502513550

Offset: 0

Author

Wolfdieter Lang, Mar 16 2001

Keywords

• nonn
• easy
• tabl

Comments

The row polynomials p(n,x) (rising powers of x) appear as numerators of the column g.f.s of triangle A060058.

First column (m=0) gives A000364 (Euler numbers). See A091742, A091743, A091744 for columns m=1..3.

The main diagonal gives A001818. The row sums give A052502. The alternating row sums give A091745.

Examples

			Triangle begins:
  {1};
  {1,1};
  {5,26,9};     <-- p(2,n)=5+26*x+9*x^2.
  {61,775,1179,225};
  ...
		

Links

• W. Lang, First 8 rows.

Formula

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