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A113408 Riordan array (1/(1-x^2-x^4*c(x^4)),x*c(x^2)), c(x) the g.f. of A000108.

%I A113408 #6 Mar 10 2017 03:01:20
%S A113408 1,0,1,1,0,1,0,2,0,1,2,0,3,0,1,0,6,0,4,0,1,3,0,12,0,5,0,1,0,12,0,20,0,
%T A113408 6,0,1,6,0,30,0,30,0,7,0,1,0,30,0,60,0,42,0,8,0,1,10,0,90,0,105,0,56,
%U A113408 0,9,0,1,0,60,0,210,0,168,0,72,0,10,0,1,20,0,210,0,420,0,252,0,90,0,11,0,1
%N A113408 Riordan array (1/(1-x^2-x^4*c(x^4)),x*c(x^2)), c(x) the g.f. of A000108.
%C A113408 Row sums are A113409. Diagonal sums are A005773(n+1) with interpolated zeros.
%H A113408 G. C. Greubel, <a href="/A113408/b113408.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A113408 T(n, k) = C((n+k)/2,k)*C(floor((n-k)/2),floor((n-k)/4))(1+(-1)^(n-k))/2.
%e A113408 Triangle begins
%e A113408 1;
%e A113408 0,1;
%e A113408 1,0,1;
%e A113408 0,2,0,1;
%e A113408 2,0,3,0,1;
%e A113408 0,6,0,4,0,1;
%e A113408 3,0,12,0,5,0,1;
%t A113408 Table[Binomial[(n + k)/2, k]*Binomial[Floor[(n - k)/2], Floor[(n - k)/4]]*(1 + (-1)^(n - k))/2, {n, 0, 49}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Mar 09 2017 *)
%o A113408 (PARI) for(n=0,25, for(k=0,n, print1( binomial((n+k)/2,k) *binomial(floor((n-k)/2),floor((n-k)/4))*(1+(-1)^(n-k))/2, ", "))) \\ _G. C. Greubel_, Mar 09 2017
%K A113408 easy,nonn,tabl
%O A113408 0,8
%A A113408 _Paul Barry_, Oct 28 2005