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%I #13 Oct 23 2014 19:43:17
%S 1,1,3,18,216,5589,336555,49768101,18707873562,18299531019402,
%T 47379925800261099,328983441917303863134,6190598463101580564238419,
%U 318441251661562459898972204796,45106336219710244780433937129788943
%N Number of partitions of 3^n-1 into powers of 3, also equals column 0 of triangle A111840, which shifts columns left and up under matrix cube.
%C Let q=3; a(n) equals the partitions of q^n-1 into powers of q, or, the coefficient of x^(q^n-1) in 1/Product_{j>=0}(1-x^(q^j)).
%H T. D. Noe, <a href="/A111841/b111841.txt">Table of n, a(n) for n=0..40</a>
%F a(n) = [x^(3^n-1)] Product_{k>=0} 1/(1-x^(3^k)).
%o (PARI) {a(n,q=3)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^q)[i-1,1], B[i,j]=(A^q)[i-1,j-1]));));A=B);return(A[n+1,1]))}
%Y Cf. A111840, A078124 (variant).
%Y Cf. A002449.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 22 2005
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