id:A165233 - OEIS Search Results

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Signed denominators of terms in series expansion of cos(x)+sin(x)

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1, 1, -2, -6, 24, 120, -720, -5040, 40320, 362880, -3628800, -39916800, 479001600, 6227020800, -87178291200, -1307674368000, 20922789888000, 355687428096000, -6402373705728000, -121645100408832000, 2432902008176640000 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Sum(n>=0,1/a(n))=cos(1)+sin(1)` `Sum(n>=0,(Pi/4)^n/a(n))=sqrt(2)`
	FORMULA	`a(n)=(-1)^floor(n/2)n!` `a(n)=(sin(nPi/2)+cos(nPi/2))n!` `a(n)=sqrt(2)sin((2n+1)Pi/4)n!` `a(n)=sqrt(2)cos((2n-1)Pi/4)n!`
	PROGRAM	`(PARI) a(n)=(-1)^(n\2)*n!`
	CROSSREFS	`Cf. A000142, A133942, A057077, A143623, A002193.` `Sequence in context: A124355 A133942 A159333 this_sequence A074166 A130641 A129655` `Adjacent sequences: A165230 A165231 A165232 this_sequence A165234 A165235 A165236`
	KEYWORD	`frac,sign`
	AUTHOR	`Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 09 2009`

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Last modified November 25 14:49 EST 2009. Contains 167514 sequences.

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