OFFSET
0,3
FORMULA
EXAMPLE
n\k| 0 1 2 3 4 5 6 7 8 9
---+-------------------------------------------------------------------------
0 | 1
1 | 1 2
2 | 1 7 -4
3 | 1 24 -23 -8
4 | 1 76 -164 -79 16
5 | 1 235 -960 -1045 255 32
6 | 1 716 -5485 -11155 5940 831 -64
7 | 1 2166 -29816 -116480 109960 32778 -2687 -128
8 | 1 6527 -158252 -1143336 2024920 1029844 -176257 -8703 256
9 | 1 19628 -822291 -10851888 4850816 32711632 -9230829 -937812 28159 512
PROG
(PARI) lucas(p)=2*fibonacci(p+1)-fibonacci(p);
S(n, k) = (-1)^floor((k+1)/2)*(prod(j=0, k-1, fibonacci(n-j))/prod(j=1, k, fibonacci(j)));
T(n, k) = sum(j=0, k, lucas(k+1-j)^n * S(n+1, j));
tabl(m) = for (n=0, m, for (k=0, n, print1(T(n, k), ", ")); print);
tabl(9);
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Tony Foster III, Jul 26 2018
STATUS
approved