NEW YORK (Reuters) - Warren Buffett's Berkshire Hathaway Inc will pay $26 billion to buy out Burlington Northern Santa Fe Corp in a bet that the nation's largest rail company is poised to benefit from a recovering U.S. economy. The deal announced Tuesday, Buffett's biggest-ever acquisition, also represents a bet on coal and new interest in a storied but highly cyclical American industry that has tried to reinvent itself by emphasizing its ability to move goods cheaply and efficiently. The deal was priced at a premium of 31.5 percent over BNSF's closing stock price on Monday and values the railroad at $34 billion, or 18 times estimated 2010 earnings. BNSF shares jumped 28 percent in afternoon trading; other U.S. and Canadian rail shares...