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A141596 Triangle T(n,k) = 4*binomial(n,k)^2-3, read by rows, 0<=k<=n. 2
1, 1, 1, 1, 13, 1, 1, 33, 33, 1, 1, 61, 141, 61, 1, 1, 97, 397, 397, 97, 1, 1, 141, 897, 1597, 897, 141, 1, 1, 193, 1761, 4897, 4897, 1761, 193, 1, 1, 253, 3133, 12541, 19597, 12541, 3133, 253, 1, 1, 321, 5181, 28221, 63501, 63501, 28221, 5181, 321, 1, 1, 397, 8097 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums are: 1, 2, 15, 68, 265, 990, 3675, 13704, 51453, 194450, 738991, ... = 4*binomial(2n,n) -3*(n+1).
LINKS
EXAMPLE
1;
1, 1;
1, 13, 1;
1, 33, 33, 1;
1, 61, 141, 61, 1;
1, 97, 397, 397, 97, 1;
1, 141, 897, 1597, 897, 141, 1;
1, 193, 1761, 4897, 4897, 1761, 193, 1;
1, 253, 3133, 12541, 19597, 12541, 3133, 253, 1;
1, 321, 5181, 28221, 63501, 63501, 28221, 5181, 321, 1;
1, 397, 8097, 57597, 176397, 254013, 176397, 57597, 8097, 397, 1;
MATHEMATICA
Clear[t, n, m, k, l] t[n_, m_, k_, l_] := (1 + l)*Binomial[n, m]^k - l; k = 2; l = 3; Table[Table[t[n, m, k, l], {m, 0, n}], {n, 0, 10}]; Flatten[%]
Table[4Binomial[n, k]^2-3, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Dec 21 2016 *)
CROSSREFS
Cf. A109128.
Sequence in context: A066834 A010225 A060361 * A108477 A176204 A176492
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved

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Last modified July 15 18:49 EDT 2024. Contains 374333 sequences. (Running on oeis4.)