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A132047 3*A007318 - 2*A103451 as infinite lower triangular matrices.

%I A132047 #26 Jun 16 2025 08:45:59
%S A132047 1,1,1,1,6,1,1,9,9,1,1,12,18,12,1,1,15,30,30,15,1,1,18,45,60,45,18,1,
%T A132047 1,21,63,105,105,63,21,1,1,24,84,168,210,168,84,24,1,1,27,108,252,378,
%U A132047 378,252,108,27,1,1,30,135,360,630,756,630,360,135,30,1
%N A132047 3*A007318 - 2*A103451 as infinite lower triangular matrices.
%F A132047 a(n) = 3*A007318(n) - 2*A103451(n).
%F A132047 T(n,k) = 3*C(n,k)-2*(C(n,k-n)+C(n,-k)-C(0,n+k)), 0<=k<=n. [_Eric Werley_, Jul 01 2011]
%e A132047 First few rows of the triangle are:
%e A132047   1;
%e A132047   1, 1;
%e A132047   1, 6, 1;
%e A132047   1, 9, 9, 1;
%e A132047   1, 12, 18, 12, 1;
%e A132047   1, 15, 30, 30, 15, 1;
%e A132047   1, 18, 45, 60, 45, 18, 1;
%e A132047   ...
%o A132047 (PARI) T(n, k) = my(bnk = binomial(n, k)); 3*bnk - 2*(bnk==1); \\ _Michel Marcus_, Jun 16 2022
%Y A132047 Cf. A007318, A103451, A131128 (row sums).
%K A132047 nonn,tabl,easy
%O A132047 0,5
%A A132047 _Gary W. Adamson_, Aug 08 2007
%E A132047 Corrected and extended by _Roger L. Bagula_, Nov 02 2008