OFFSET
0,2
COMMENTS
The triangle coefficients give sums of Fibonacci powers when multiplied with Lang triangle coefficients and summed (see 2nd formula).
FORMULA
EXAMPLE
n\k| 0 1 2 3 4 5 6 7 8 9
---+--------------------------------------------------
0 | 1
1 | 2 1
2 | 4 3 1
3 | 7 9 4 1
4 | 12 24 19 6 1
5 | 20 64 79 46 9 1
6 | 33 168 339 306 113 14 1
7 | 54 441 1431 2126 1205 287 22 1
8 | 88 1155 6072 14502 13581 4928 736 35 1
9 | 143 3025 25707 99587 149717 90013 20371 1905 56 1
PROG
(PARI) f(n, k) = prod(j=0, k-1, fibonacci(n-j))/prod(j=1, k, fibonacci(j));
T(n, k) = if (n< 0, 0, T(n-1, k) + f(n+1, k+1));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Jul 20 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Tony Foster III, Jul 09 2018
EXTENSIONS
More terms from Michel Marcus, Jul 20 2018
STATUS
approved