|
Search: id:A062133
|
|
|
| A062133 |
|
Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers). |
|
+0
2
|
|
| 0, 1, 2, 20, 36, 16, 456, 944, 672, 160, 14304, 33760, 28800, 10880, 1536, 575040, 1466752, 1413120, 666880, 157440, 14848, 27659520, 74774784, 79278080, 43330560, 13153280, 2128896, 143360, 1548126720
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
The row polynomials pPL1(n,x) := sum(a(n,m)*x^m,m=0..n) and pPL2(n,x) := sum(A062134(n,m)*x^m,m=0..n) appear in the k-fold convolution of the associated Pell numbers PL(n) := A001333(n+1), n >= 0, as follows: PL(k; n) := A054458(n+k,k)= (2*pPL1(k,n)*PL(n+1)+pPL2(k,n)*PL(n)/(k!*8^k), k >= 0.
|
|
EXAMPLE
|
{0}; {1,2}; {20,36,16}; {456,944,672,160}; ...
pPL1(2,n)=4*(5+9*n+4*n^2)=4*(1+n)*(5+4*n); pL2(2,n)=8*(1+3*n+2*n^2)=8*(1+n)*(1+2*n); PL(2; n)= A054460(n)=(1+n)*((5+4*n)*PL(n+1)+(1+2*n)*PL(n))/16.
|
|
CROSSREFS
|
A062134(n, m) (companion triangle), A054458(n, m) (convolution triangle).
Sequence in context: A061471 A112271 A103076 this_sequence A050684 A073214 A097652
Adjacent sequences: A062130 A062131 A062132 this_sequence A062134 A062135 A062136
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 19 2001
|
|
|
Search completed in 0.002 seconds
|
