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 A130528 Triangle T, read by rows, where row n+1 of T equals row n of matrix power T^n added to row n of T (shifted right). 3
 1, 1, 1, 2, 2, 1, 12, 8, 3, 1, 156, 80, 20, 4, 1, 3540, 1516, 300, 40, 5, 1, 123400, 46236, 7816, 840, 70, 6, 1, 6091988, 2054980, 309268, 28816, 1960, 112, 7, 1, 402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1, 34289884368, 9862677332 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS EXAMPLE Triangle begins: 1; 1, 1; 2, 2, 1; 12, 8, 3, 1; 156, 80, 20, 4, 1; 3540, 1516, 300, 40, 5, 1; 123400, 46236, 7816, 840, 70, 6, 1; 6091988, 2054980, 309268, 28816, 1960, 112, 7, 1; 402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1; ... Matrix square T^2 begins: 1; 2, 1; 6, 4, 1; 38, 22, 6, 1; 480, 232, 52, 8, 1; ... [Row 2 of T] = [row 1 of T^2, 0] + [0, row 1 of T]: [2, 2, 1] = [2, 1, 0] + [0, 1, 1]. Matrix cube T^3 begins: 1; 3, 1; 12, 6, 1; ... [Row 3 of T] = [row 2 of T^3, 0] + [0, row 2 of T]: [12, 8, 3, 1] = [12, 6, 1, 0] + [0, 2, 2, 1]. Matrix 4th power T^4 begins: 1; 4, 1; 20, 8, 1; 156, 68, 12, 1; ... [Row 4 of T] = [row 3 of T^4, 0] + [0, row 3 of T]: [156, 80, 20, 4, 1] = [156, 68, 12, 1, 0] + [0, 12, 8, 3, 1]. PROG (PARI) T(n, k)=local(M=Mat(1)); if(n=c && r<=n, T(r-1, c-1)))); T(n-1, k-1)+(M^n)[n, k+1])) CROSSREFS Columns: A130529, A130530, A130531. Sequence in context: A014846 A100942 A132471 * A132986 A019112 A276851 Adjacent sequences:  A130525 A130526 A130527 * A130529 A130530 A130531 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jun 02 2007 STATUS approved

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