OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
EXAMPLE
Triangle begins as:
1;
1, 1;
5, 3, 1;
13, 9, 5, 1;
49, 31, 17, 7, 1;
161, 105, 61, 29, 9, 1;
581, 371, 217, 111, 45, 11, 1;
MAPLE
A115991 := proc(n, k)
add(binomial(n-k, j-k)*binomial(j, n-j)*2^(n-j), j=0..n) ;
end proc:
seq(seq(A115991(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Jun 25 2023
MATHEMATICA
Table[Sum[Binomial[n-k, j-k]*Binomial[j, n-j]*2^(n-j), {j, 0, n}], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, May 09 2019 *)
PROG
(PARI) {T(n, k) = sum(j=0, n, binomial(n-k, j-k)*binomial(j, n-j)*2^(n-j))}; \\ G. C. Greubel, May 09 2019
(Magma) [[(&+[Binomial(n-k, j-k)*Binomial(j, n-j)*2^(n-j): j in [0..n]]): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 09 2019
(Sage) [[sum(binomial(n-k, j-k)*binomial(j, n-j)*2^(n-j) for j in (0..n)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, May 09 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> Sum([0..n], j-> Binomial(n-k, j-k)*Binomial(j, n-j)*2^(n-j)) ))); # G. C. Greubel, May 09 2019
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 10 2006
STATUS
approved