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A135091 A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n.

%I A135091 #19 Mar 28 2022 08:15:08
%S A135091 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 A135091 141,1,7,63,245,665,1071,987,393,1,8,84,392,1330,2856,3948,3144,1107,
%U A135091 1,9,108,588,2394,6426,11844,14148,9963,3139
%N A135091 A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n.
%C A135091 Right border = A002426.
%C A135091 Row sums = A000984: (1, 2, 6, 20, 70, 252, ...).
%C A135091 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 A135091 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 A135091 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 A135091 See A098473.
%e A135091 First few rows of the triangle:
%e A135091   1;
%e A135091   1, 1;
%e A135091   1, 2,  3;
%e A135091   1, 3,  9,   7;
%e A135091   1, 4, 18,  28,  19;
%e A135091   1, 5, 30,  70,  95,   51;
%e A135091   1, 6, 45, 140, 285,  306, 141;
%e A135091   1, 7, 63, 245, 665, 1071, 987, 393;
%e A135091   ...
%Y A135091 Cf. A002426, A000984, A098473.
%K A135091 nonn,tabl
%O A135091 0,5
%A A135091 _Gary W. Adamson_, Nov 18 2007