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A060063
Triangle of coefficients of certain polynomials used for G.f.s of columns of triangle A060058.
10
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.
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
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Mar 16 2001
STATUS
approved