%I #14 Sep 08 2022 08:45:14
%S 1,0,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,5,1,0,0,0,0,0,15,1,0,0,0,0,0,0,
%T 35,1,0,0,0,0,0,0,1,70,1,0,0,0,0,0,0,0,9,126,1,0,0,0,0,0,0,0,0,45,210,
%U 1,0,0,0,0,0,0,0,0,0,165,330,1,0,0,0,0,0,0,0,0,0,1,495,495,1
%N Triangle T(n,k) with diagonals T(n,n-k) = binomial(n, 4k).
%C Row sums are A038503.
%H Seiichi Manyama, <a href="/A098173/b098173.txt">Rows n = 0..139, flattened</a>
%F Triangle T(n, k) = binomial(n, 4(n-k)).
%e Rows begin
%e {1},
%e {0,1},
%e {0,0,1},
%e {0,0,0,1},
%e {0,0,0,1,1},
%e {0,0,0,0,5,1},
%e ...
%t Table[Binomial[n, 4(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Mar 15 2019 *)
%o (PARI) {T(n, k) = binomial(n, 4*(n-k))}; \\ _G. C. Greubel_, Mar 15 2019
%o (Magma) [[Binomial(n, 4*(n-k)): k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Mar 15 2019
%o (Sage) [[binomial(n, 4*(n-k)) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Mar 15 2019
%o (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 4*(n-k)) ))); # _G. C. Greubel_, Mar 15 2019
%Y Cf. A098158, A098172.
%K easy,nonn,tabl
%O 0,20
%A _Paul Barry_, Aug 30 2004