cp's OEIS Frontend

A373717 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..floor(k*n/(2*k+1))} binomial(k * (n-2*j),j).

%I A373717 #15 Jun 15 2024 09:23:10
%S A373717 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,3,1,1,1,1,4,5,4,1,1,1,1,5,7,8,
%T A373717 6,1,1,1,1,6,9,13,15,9,1,1,1,1,7,11,19,28,26,13,1,1,1,1,8,13,26,45,53,
%U A373717 45,19,1,1,1,1,9,15,34,66,91,105,80,28,1,1,1,1,10,17,43,91,141,201,211,140,41,1
%N A373717 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..floor(k*n/(2*k+1))} binomial(k * (n-2*j),j).
%F A373717 G.f. of column k: 1/(1 - x * (1 + x^2)^k).
%F A373717 T(n,k) = Sum_{j=0..k} binomial(k,j) * T(n-2*j-1,k).
%e A373717 Square array begins:
%e A373717   1, 1,  1,  1,  1,  1,  1, ...
%e A373717   1, 1,  1,  1,  1,  1,  1, ...
%e A373717   1, 1,  1,  1,  1,  1,  1, ...
%e A373717   1, 2,  3,  4,  5,  6,  7, ...
%e A373717   1, 3,  5,  7,  9, 11, 13, ...
%e A373717   1, 4,  8, 13, 19, 26, 34, ...
%e A373717   1, 6, 15, 28, 45, 66, 91, ...
%o A373717 (PARI) T(n, k) = sum(j=0, k*n\(2*k+1), binomial(k*(n-2*j), j));
%Y A373717 Columns k=0..3 give A000012, A000930, A193147, A373718.
%Y A373717 Main diagonal gives A373719.
%Y A373717 Cf. A099233.
%K A373717 nonn,tabl
%O A373717 0,14
%A A373717 _Seiichi Manyama_, Jun 15 2024