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%I #7 Mar 30 2012 18:36:32
%S 1,3,12,93,1632,68457,7112055,1879090014,1287814075131,
%T 2325758241901161,11213788533232011006,145939965725683888932081,
%U 5174322925070232320838406581,503750821963423009552527526376232
%N Second column, M(n+1,1) for n>=0, of infinite lower triangular matrix M defined in A078122.
%H Alois P. Heinz, <a href="/A078124/b078124.txt">Table of n, a(n) for n = 0..40</a>
%F The partitions of 2*3^n into powers of 3, or, the coefficient of x^(2*3^n) in 1/Product_{j=0..inf}(1-x^(3^j)) (conjecture).
%e a(1)=3 since the coefficient of x^6 in 1/Product_{j=0..inf}(1-x^(3^j)) = 1 + x + x^2 + 2x^3 + 2x^4 + 2x^5 + 3x^6 + ... is 3.
%t m[i_, j_] := m[i, j]=If[j==0||i==j, 1, m3[i-1, j-1]]; m2[i_, j_] := m2[i, j]=Sum[m[i, k]m[k, j], {k, j, i}]; m3[i_, j_] := m3[i, j]=Sum[m[i, k]m2[k, j], {k, j, i}]; a[n_] := m[n+1, 1]
%Y Cf. A078121, A078122 (matrix shift when cubed), A078123, A078125.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 18 2002
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