|
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
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 A091742-4 for columns m=1..3.
The main diagonal gives A001818. The row sums give A052502. The alternating row sums give A091745.
|
|
|
LINKS
| W. Lang, First 8 rows.
|
|
|
FORMULA
| The row polynomials p(n, x) := sum(a(n, m)*x^m, m=0..n) satisfy the differential difference eq.: p(n, x)=x*((1-x)^2)*diff(p(n-1, x), x$2) + (1+6*(n-1)*x+(5-6*n)*x^2)*diff(p(n-1, x), x) + (3*n-2)*(1+(3*n-2)*x)*p(n-1, x), n>=1, with input p(0, x)=1. Added by W. Lang, Feb 13 2004.
|
|
|
EXAMPLE
| {1}; {1,1}; {5,26,9}; {61,775,1179,225}; ... p(2,n)=5+26*x+9*x^2.
|
|
|
CROSSREFS
| Sequence in context: A099077 A137113 A137115 * A106295 A057688 A048269
Adjacent sequences: A060060 A060061 A060062 * A060064 A060065 A060066
|
|
|
KEYWORD
| nonn,easy,tabl
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 16 2001
|
| |
|
|
