OFFSET
1,2
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
Sum_{k=1..n} T(n, k) = A002417(n).
T(n, n) = A002411(n).
From G. C. Greubel, Jul 12 2022: (Start)
T(n, k) = n * binomial(k+1, 2).
Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = (1/4)*(4*n - 3*floor((n+1)/2) + 3)*binomial(2 + floor((n+1)/2), 3).
T(2*n-1, n) = A002414(n), n >= 1.
T(2*n-2, n-1) = A011379(n-1), n >= 2. (End)
EXAMPLE
First few rows of the triangle =
1;
2, 6;
3, 9, 18;
4, 12, 24, 40;
5, 15, 30, 50, 75;
6, 18, 36, 60, 90, 126;
7, 21, 42, 70, 105, 147, 196;
...
MATHEMATICA
Table[n*Binomial[k+1, 2], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Jul 12 2022 *)
PROG
(Magma) [n*Binomial(k+1, 2): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 12 2022
(SageMath) flatten([[n*binomial(k+1, 2) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Jul 12 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jul 30 2008
STATUS
approved
