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A110197
Number triangle of sums of squared binomial coefficients.
1
1, 2, 1, 3, 5, 1, 4, 14, 10, 1, 5, 30, 46, 17, 1, 6, 55, 146, 117, 26, 1, 7, 91, 371, 517, 251, 37, 1, 8, 140, 812, 1742, 1476, 478, 50, 1, 9, 204, 1596, 4878, 6376, 3614, 834, 65, 1, 10, 285, 2892, 11934, 22252, 19490, 7890, 1361, 82, 1, 11, 385, 4917, 26334, 66352
OFFSET
0,2
COMMENTS
Alternatively, number square T(n,k) = Sum_{i=0..n} binomial(i+k,k)^2 read by antidiagonals. Columns include A000027, A000330, A024166, A086020, A086023, A086025. Row sums are A006134. Diagonal sums are A110198.
FORMULA
Number triangle T(n,k) = Sum_{i=0..n-k} binomial(i+k,k)^2.
EXAMPLE
Rows start
1;
2, 1;
3, 5, 1;
4, 14, 10, 1;
5, 30, 46, 17, 1;
6, 55, 146, 117, 26, 1;
PROG
(PARI) T(n, k) = sum(i=0, n-k, binomial(i+k, k)^2);
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print(); ); \\ Michel Marcus, Dec 03 2016
CROSSREFS
Sequence in context: A104029 A208752 A119308 * A124819 A124019 A337886
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jul 15 2005
STATUS
approved