OFFSET
1,5
COMMENTS
Row sums are: {1, 2, 7, 34, 166, 652, 2799, 11226, 48934, 178956, ...}.
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k, q) = Sum_{j=0..10} q^j * floor( binomial(n+1,k)*binomial(n-1,k-1)/(2^j*(n+1)) ) for q = 2.
EXAMPLE
The triangle begins as:
1;
1, 1;
1, 5, 1;
1, 16, 16, 1;
1, 36, 92, 36, 1;
1, 49, 276, 276, 49, 1;
1, 93, 673, 1265, 673, 93, 1;
1, 124, 1484, 4004, 4004, 1484, 124, 1;
1, 204, 2832, 12400, 18060, 12400, 2832, 204, 1;
1, 237, 5244, 26416, 57580, 57580, 26416, 5244, 237, 1;
MATHEMATICA
T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n-1, k-1]*Binomial[n+1, k]/(2^j*(n+1))], {j, 0, 10}];
Table[T[n, k, 2], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 16 2021 *)
PROG
(Magma)
T:= func< n, k, q | (&+[ q^j*Floor( Binomial(n+1, k)*Binomial(n-1, k-1)/(2^j*(n+1)) ): j in [0..10]]) >;
[T(n, k, 2): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 16 2021
(Sage)
def T(n, k, q): return sum( q^j*( (binomial(n+1, k)*binomial(n-1, k-1)//(2^j*(n+1))) ) for j in (0..10))
flatten([[T(n, k, 2) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 16 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 06 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 16 2021
STATUS
approved