id:A102584 - OEIS Search Results

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1/2 times the cancellation factor in reducing Sum_{k=0 to 2n+1} 1/k! to lowest terms.

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1, 1, 10, 5, 4, 1, 2, 65, 2000, 1, 26, 247, 20, 5, 2, 19, 8, 115, 10, 23, 52, 31, 10, 65, 416, 37, 2, 25, 20, 1, 38, 1, 40, 325, 1406, 37, 676, 65, 10, 63829, 368, 1, 230, 5, 4, 1, 26, 5, 40, 247, 26, 43, 3100, 9785, 2, 1, 256, 5, 2050, 13, 388, 1, 4810, 1495, 8, 23, 254, 5 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`The denominator of Sum_{k=0 to m} 1/k! is m!/d, where d = A093101(m). If m = 2n+1 > 1, then d is even and a(n) = d/2.`
	REFERENCES	`J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly, 113 (2006) 637-641.`
	LINKS	`Index entries for sequences related to factorial numbers.`
	FORMULA	`a(n) = GCD(m!, 1+m+m(m-1)+m(m-1)(m-2)+...+m!)/2, where m = 2n+1.`
	EXAMPLE	`1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! = 13700/5040 = (20685)/(20252) and 7 = 2*3+1, so a(3) = 20/2 = 10.`
	CROSSREFS	`a(n) = A093101(2n+1)/2 = (2n+1)!/(2*A061355(2n+1)).` `See also A102581, A102582.` `Adjacent sequences: A102581 A102582 A102583 this_sequence A102585 A102586 A102587` `Sequence in context: A050020 A053050 A033330 this_sequence A134167 A080461 A066578`
	KEYWORD	`nonn`
	AUTHOR	`Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 22 2005`

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Last modified October 13 02:37 EDT 2008. Contains 145008 sequences.

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