|
Search: id:A057282
|
|
|
| A057282 |
|
Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057281. |
|
+0
3
|
|
| 2, 5, 17, 15, 120, 225, 50, 700, 3050, 4080, 175, 3775, 28625, 89225, 94440, 625, 19225, 223175, 1208975, 3006000, 2666880, 2250, 93500, 1537100, 12689800, 54824650, 115299900, 89016480, 8125, 438250, 9670750, 112454500, 737744125
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..
The k-th convolution of F0(n) := A000045(n+1), n >= 0, (Fibonacci numbers starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^k), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A057281(k,m).
a(k,0)= A020876(k), k >= 0.
|
|
EXAMPLE
|
k=2: F2(n)=((5*n^2+21*n+16)*F(n+2)+(5*n^2+27*n+34)*F(n+1))/50, F(n) := A000045(n); see A001628.
2; 5,17; 15,120,225; 50,700,3050,4080; 175,3775,28625,89225,94440; ...
|
|
CROSSREFS
|
Cf. A000045, A037027, A057995, A057280, A057281.
Row sums: A151615.
Sequence in context: A115894 A033835 A005529 this_sequence A123364 A025553 A075544
Adjacent sequences: A057279 A057280 A057281 this_sequence A057283 A057284 A057285
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2000
|
|
|
Search completed in 0.002 seconds
|
