cp's OEIS Frontend

A348593 Triangle read by rows: T(n,m) = Sum_{j=0..min(m,n-m)} C(2j,j)*C(n-2j-1,m-j)*C(n-m,j)/(j+1).

%I A348593 #24 Jan 27 2022 21:02:12
%S A348593 1,1,1,2,1,4,1,1,6,7,1,1,8,18,6,1,1,10,34,30,7,1,1,12,55,88,33,8,1,1,
%T A348593 14,81,195,145,42,9,1,1,16,112,366,460,184,52,10,1,1,18,148,616,1146,
%U A348593 763,248,63,11,1,1,20,189,960,2422,2544,1060,324,75,12,1,1,22,235,1413,4558,6916,4282,1490,413,88,13,1
%N A348593 Triangle read by rows: T(n,m) = Sum_{j=0..min(m,n-m)} C(2j,j)*C(n-2j-1,m-j)*C(n-m,j)/(j+1).
%F A348593 G.f.: (1-sqrt(1-4*x^2*y*(1-x*y)/(1-x-x*y)))/(2*x^2*y).
%F A348593 Sum_{m>=0} (-1)^m * T(n,m) = A307374(n). - _Alois P. Heinz_, Jan 26 2022
%e A348593 Triangle begins
%e A348593   1;
%e A348593   1;
%e A348593   1,  2;
%e A348593   1,  4,  1;
%e A348593   1,  6,  7,  1;
%e A348593   1,  8, 18,  6,  1;
%e A348593   1, 10, 34, 30,  7,  1;
%e A348593   1, 12, 55, 88, 33,  8,  1;
%o A348593 (Maxima) T(n,m):=sum(binomial(2*j,j)*binomial(n-2*j-1,m-j)*binomial(n-m,j)/(j+1), j,0,min(m,n-m));
%Y A348593 Row sums give A173992.
%Y A348593 Cf. A000108, A307374.
%K A348593 nonn,tabf
%O A348593 0,4
%A A348593 _Vladimir Kruchinin_, Jan 25 2022