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Main diagonal of square table A113081; also, a(n) equals the n-th term in column 0 of the matrix n-th power of triangle A113084.
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%I #3 Mar 30 2012 18:36:51

%S 1,1,10,331,33476,10204145,9378590446,26026690264407,

%T 218132378185337416,5518274388618175447069,

%U 421034872020570533423509010,96809747319527667989371938562883

%N Main diagonal of square table A113081; also, a(n) equals the n-th term in column 0 of the matrix n-th power of triangle A113084.

%o (PARI) {a(n,q=3)=local(M=matrix(n+1,n+1));for(r=1,n+1, for(c=1,r, M[r,c]=if(r==c,1,if(c>1,(M^q)[r-1,c-1])+(M^q)[r-1,c]))); return((M^n)[n+1,1])}

%Y Cf. A113081, A113084.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 14 2005