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%I A175012 #7 Jul 20 2017 01:53:44
%S A175012 1,2,2,3,2,4,4,2,4,9,5,2,4,10,14,6,2,4,10,19,23,7,2,4,10,20,34,32,8,2,
%T A175012 4,10,20,39,55,46,9,2,4,10,20,40,66,88,60,10
%N A175012 Triangle generated from the g.f of A000712 (i.e., 1/(1-x^m)^2) interleaved with zeros.
%C A175012 Row sums of the triangle = A000712.
%F A175012 Given 1/(1-x^m)^2 = S(x) = (1 + 2x + 3x^2 + ...), let a = S(x), b = S(x^2) (i.e., S(x) interleaved with one zero); S(x^3) = S(x) interleaved with two zeros = c, etc.; then row 1 = a, row 2 = a*b, row 3 = a*b*c, ...
%F A175012 Take finite differences of the array from the top down, becoming rows of the triangle.
%e A175012 First few rows of the array =
%e A175012   1, 2, 3,  4,  5,  6,  7,   8,   9,  10, ...
%e A175012   1, 2, 5,  8, 14, 20, 30,  40,  55,  70, ...
%e A175012   1, 2, 5, 10, 18, 30, 49,  74, 110, 158, ...
%e A175012   1, 2, 5, 10, 20, 34, 59,  94, 149, 224, ...
%e A175012   1, 2, 5, 10, 20, 36, 63, 104, 169, 264, ...
%e A175012   1, 2, 5, 10, 20, 36, 65, 108, 179, 284, ...
%e A175012   ...
%e A175012 First few rows of the triangle =
%e A175012   1;
%e A175012   2;
%e A175012   2,  3;
%e A175012   2,  4,  4;
%e A175012   2,  4,  9,  5;
%e A175012   2,  4, 10, 14,  6;
%e A175012   2,  4, 10, 19, 23,  7;
%e A175012   2,  4, 10, 20, 34, 32,  8;
%e A175012   2,  4, 10, 20, 39, 55, 46,  9;
%e A175012   2,  4, 10, 20, 40, 66, 88, 60, 10;
%e A175012   ...
%Y A175012 Cf. A000712.
%K A175012 nonn,tabl,more
%O A175012 0,2
%A A175012 _Gary W. Adamson_, Apr 03 2010

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