A348593 - OEIS

%I #24 Jan 27 2022 21:02:12

%S 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 14,81,195,145,42,9,1,1,16,112,366,460,184,52,10,1,1,18,148,616,1146,

%U 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 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 G.f.: (1-sqrt(1-4*x^2*y*(1-x*y)/(1-x-x*y)))/(2*x^2*y).

%F Sum_{m>=0} (-1)^m * T(n,m) = A307374(n). - _Alois P. Heinz_, Jan 26 2022

%e Triangle begins

%e   1;

%e   1;

%e   1,  2;

%e   1,  4,  1;

%e   1,  6,  7,  1;

%e   1,  8, 18,  6,  1;

%e   1, 10, 34, 30,  7,  1;

%e   1, 12, 55, 88, 33,  8,  1;

%o (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 Row sums give A173992.

%Y Cf. A000108, A307374.

%K nonn,tabf

%O 0,4

%A _Vladimir Kruchinin_, Jan 25 2022