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A272868
Triangle read by rows, T(n,k) = 2^k*GegenbauerC(k,-n,-1/4), for n>=0 and 0<=k<=n.
0
1, 1, 1, 1, 2, 9, 1, 3, 15, 25, 1, 4, 22, 52, 145, 1, 5, 30, 90, 285, 561, 1, 6, 39, 140, 495, 1206, 2841, 1, 7, 49, 203, 791, 2261, 6027, 12489, 1, 8, 60, 280, 1190, 3864, 11452, 27560, 60705, 1, 9, 72, 372, 1710, 6174, 20076, 54468, 134073, 281185
OFFSET
0,5
FORMULA
T(n,n) = A084605(n).
T(n,n-1) = A098520(n).
T(n+1,n)/(n+1) = A091147(n).
EXAMPLE
Triangle starts:
1;
1, 1;
1, 2, 9;
1, 3, 15, 25;
1, 4, 22, 52, 145;
1, 5, 30, 90, 285, 561;
1, 6, 39, 140, 495, 1206, 2841;
1, 7, 49, 203, 791, 2261, 6027, 12489;
MAPLE
T := (n, k) -> simplify(2^k*GegenbauerC(k, -n, -1/4)):
for n from 0 to 9 do seq(T(n, k), k=0..n) od;
MATHEMATICA
Table[If[n == 0, 1, 2^k GegenbauerC[k, -n, -1/4]], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, May 08 2016 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 08 2016
STATUS
approved