%I #19 Mar 28 2022 08:15:08

%S 1,1,1,1,2,3,1,3,9,7,1,4,18,28,19,1,5,30,70,95,51,1,6,45,140,285,306,

%T 141,1,7,63,245,665,1071,987,393,1,8,84,392,1330,2856,3948,3144,1107,

%U 1,9,108,588,2394,6426,11844,14148,9963,3139

%N A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n.

%C Right border = A002426.

%C Row sums = A000984: (1, 2, 6, 20, 70, 252, ...).

%C The n-th row of this triangle lists the coefficients of the polynomial: p := (1/Pi)*Integral_{s=0..Pi} (1 + t - 2*t*cos(s))^n; Pi / 1 | n p := ---- | (1 + t - 2 t cos(s)) ds Pi | / 0 for example n=5 then 4 2 3 p = 19 t + 18 t + 28 t + 4 t + 1. - _Theodore Kolokolnikov_, Oct 09 2010

%F A007318 * triangle M, where M = A002426 * 0^(n-k), 0 <= k <= n; i.e., M = an infinite lower triangular matrix with A002426 as the right border and the rest zeros.

%F O.g.f. appears to be (1/sqrt(1-t*(1-x)))*1/sqrt(1-t*(1+3*x)) = 1 + (1+x)*t + (1 + 2*x + 3*x^2)*t^2 + ....

%F See A098473.

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 1, 2, 3;

%e 1, 3, 9, 7;

%e 1, 4, 18, 28, 19;

%e 1, 5, 30, 70, 95, 51;

%e 1, 6, 45, 140, 285, 306, 141;

%e 1, 7, 63, 245, 665, 1071, 987, 393;

%e ...

%Y Cf. A002426, A000984, A098473.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Nov 18 2007