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 A121391 Triangle T, read by rows, where column k equals column k of T^(k+1) shift down 1 row, with T(n,n)=T(n+1,n)=1 for n>=0. 3
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 15, 12, 4, 1, 1, 1, 55, 58, 22, 5, 1, 1, 1, 252, 333, 146, 35, 6, 1, 1, 1, 1449, 2268, 1131, 295, 51, 7, 1, 1, 1, 10305, 18281, 10120, 2870, 521, 70, 8, 1, 1, 1, 88611, 173127, 104015, 31731, 6096, 840, 92, 9, 1, 1, 1, 901204 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS EXAMPLE Triangle T begins: 1; 1, 1; 1, 1, 1; 1, 2, 1, 1; 1, 5, 3, 1, 1; 1, 15, 12, 4, 1, 1; 1, 55, 58, 22, 5, 1, 1; 1, 252, 333, 146, 35, 6, 1, 1; 1, 1449, 2268, 1131, 295, 51, 7, 1, 1; 1, 10305, 18281, 10120, 2870, 521, 70, 8, 1, 1; 1, 88611, 173127, 104015, 31731, 6096, 840, 92, 9, 1, 1; ... where column 0 of T^1 shift down 1 row equals column 0 of T. The matrix square T^2 begins: 1; 2, 1; 3, 2, 1; 5, 5, 2, 1; 11, 15, 7, 2, 1; 34, 55, 31, 9, 2, 1; 143, 252, 165, 53, 11, 2, 1; ... where column 1 of T^2 shift down 1 row equals column 1 of T. The matrix cube T^3 begins: 1; 3, 1; 6, 3, 1; 13, 9, 3, 1; 36, 31, 12, 3, 1; 132, 129, 58, 15, 3, 1; 627, 663, 333, 94, 18, 3, 1; ... where column 2 of T^3 shift down 1 row equals column 2 of T. PROG (PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(A^j)[i-1, j]); )); A=B); return(A[n+1, k+1])} CROSSREFS Cf. A121392 (column 1), A121393 (column 2), A121394 (column 3); variant: A121395. Sequence in context: A090182 A256384 A111673 * A241194 A008326 A181196 Adjacent sequences:  A121388 A121389 A121390 * A121392 A121393 A121394 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jul 27 2006 STATUS approved

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