%I #12 Oct 11 2021 18:43:50
%S 1,3,1,6,3,1,10,6,5,1,15,10,15,5,1,21,15,35,15,7,1,28,21,70,35,28,7,1,
%T 36,28,126,70,84,28,9,1,45,36,210,126,210,84,45,9,1,55,45,330,210,462,
%U 210,165,45,11,1
%N A000012 * A133084.
%C Row sums give A033484.
%C Duplicate of A133093. - _Georg Fischer_, Oct 10 2021
%F A000012 * A133084 as infinite lower triangular matrices.
%e First few rows of the triangle are:
%e 1;
%e 3, 1;
%e 6, 3, 1;
%e 10, 6, 5, 1;
%e 15, 10, 15, 5, 1;
%e 21, 15, 35, 15, 7, 1;
%e 28, 21, 70, 35, 28, 7, 1;
%e ...
%o (PARI) T4(n, k) = if(k == n, 1, (1 - (1 + (-1)^k)/2 )*binomial(n, k) + ((1 + (-1)^k)/2)*binomial(n - 1, k - 1)); \\ A133084
%o N=10; matrix(N, N, n, k, if(n>=k, 1))*matrix(N, N, n, k, T4(n,k)) \\ _Michel Marcus_, Oct 11 2021
%Y Cf. A133084, A033484.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Sep 08 2007
%E a(46) corrected by _Georg Fischer_, Oct 10 2021