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A127967 A right-skewed Pascal triangle, with interspersed 1's on main diagonal.

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%I A127967 #11 Jun 12 2024 06:56:12
%S A127967 1,1,1,1,0,1,1,0,2,1,1,0,3,0,1,1,0,4,0,3,1,1,0,5,0,6,0,1,1,0,6,0,10,0,
%T A127967 4,1,1,0,7,0,15,0,10,0,1,1,0,8,0,21,0,20,0,5,1,1,0,9,0,28,0,35,0,15,0,
%U A127967 1,1,0,10,0,36,0,56,0,35,0,6,1
%N A127967 A right-skewed Pascal triangle, with interspersed 1's on main diagonal.
%C A127967 Linked to Fibonacci numbers by row sums A127968. Inverse A127969 is linked to Genocchi numbers by its first column.
%F A127967 Column k is generated by x^(-2)*(x*(1-x)^(-1/2))^(k+2), where non-integer values are set to 0; or, column k has g.f. x^k/(1-x)^(1+k/2) if k is even, x^k if k is odd.
%e A127967 Triangle begins
%e A127967   1;
%e A127967   1, 1;
%e A127967   1, 0,  1;
%e A127967   1, 0,  2, 1;
%e A127967   1, 0,  3, 0,  1;
%e A127967   1, 0,  4, 0,  3, 1;
%e A127967   1, 0,  5, 0,  6, 0,  1;
%e A127967   1, 0,  6, 0, 10, 0,  4, 1;
%e A127967   1, 0,  7, 0, 15, 0, 10, 0,  1;
%e A127967   1, 0,  8, 0, 21, 0, 20, 0,  5, 1;
%e A127967   1, 0,  9, 0, 28, 0, 35, 0, 15, 0,  1;
%e A127967   1, 0, 10, 0, 36, 0, 56, 0, 35, 0,  6, 1;
%e A127967   1, 0, 11, 0, 45, 0, 84, 0, 70, 0, 21, 0, 1;
%Y A127967 Cf. A127968, A127969.
%K A127967 easy,nonn,tabl
%O A127967 0,9
%A A127967 _Paul Barry_, Feb 09 2007