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

0,4

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.

Links

Table of n, a(n) for n=0..26.

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

Example

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

Crossrefs

Sequence in context: A099077 A137113 A137115 * A106295 A057688 A259207

Adjacent sequences: A060060 A060061 A060062 * A060064 A060065 A060066

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Mar 16 2001

Status

approved