OFFSET
0,2
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = A117418(n+k+1, 2*k+1). - G. C. Greubel, May 31 2021
EXAMPLE
Triangle T begins:
1;
2, 1;
4, 4, 1;
9, 14, 6, 1;
23, 50, 28, 8, 1;
66, 191, 126, 48, 10, 1;
209, 780, 572, 264, 70, 12, 1;
724, 3415, 2692, 1440, 438, 98, 14, 1;
2722, 15924, 13203, 7990, 2646, 698, 130, 16, 1;
11054, 78595, 67542, 45566, 15920, 4702, 1029, 168, 18, 1;
The matrix square-root T^(1/2) = A117418, which begins:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 9, 8, 4, 1;
1, 23, 22, 14, 5, 1;
1, 66, 65, 50, 20, 6, 1;
1, 209, 208, 191, 79, 28, 7, 1;
where column 2k+1 of T^(1/2) equals column k of T for k>=0.
MATHEMATICA
PROG
(Sage)
@CachedFunction
def A117418(n, k):
if (k<0 or k>n): return 0
elif (k==0 or k==n): return 1
elif (k==n-1): return n
flatten([[A117427(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 31 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 14 2006
STATUS
approved