A091744 -id:A091744

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A060063

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

+10
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

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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};

...

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Mar 16 2001

STATUS

approved

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