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Column 6 of table A125790; also equals row sums of matrix power A078121^6.
8

%I #7 Mar 17 2023 21:48:02

%S 1,7,49,455,6321,140231,5174449,326603719,35994670257,7036275790791,

%T 2470183452677297,1573137497080468423,1832597507832323118257,

%U 3932481446278522861786055,15637033863127787477309461681,115814953429924513361085880079303,1604893891765170672173387008222303409

%N Column 6 of table A125790; also equals row sums of matrix power A078121^6.

%C Triangle A078121 shifts left one column under matrix square and is related to partitions into powers of 2.

%o (PARI) a(n)=local(p=6,q=2,A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i || j==1, B[i, j]=1, B[i, j]=(A^q)[i-1, j-1]); )); A=B); return(sum(c=0,n,(A^p)[n+1,c+1]))

%Y Cf. A125790, A078121; columns: A002577, A125792, A125793, A125794, A125795; diagonals: A125797, A125798.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 10 2006