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%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