A138761 - OEIS

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A138761

a(n) is the smallest member of A000522 divisible by 2^n, where A000522(m) = total number of arrangements of a set with m elements.

1, 2, 16, 16, 16, 330665665962404000, 4216377920843140187197325631474390438452208808916276571342090223552, 795122903356221671989686583483030190065987827171594852730733417837764474360219351256063288666704695687102866008496014152766550264566952850218752219114140781400452987113610891553002103768576 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`a(n) < A000522(2^n) for n > 0; see Sondow and Schalm, Proposition A.13 part (ii).`
	REFERENCES	`J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.`
	LINKS	`J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II` `Index entries for sequences related to factorial numbers`
	FORMULA	`a(n) = A000522(A127014(n)) = Sum_{k=0...A127014(n)} A127014(n)!/k! for n > 0.`
	EXAMPLE	`a(5) = A000522(19) = 330665665962404000 because that is the smallest member of A000522 divisible by 2^5.`
	CROSSREFS	`Cf. A000522, A127014, A127015.` `Sequence in context: A110008 A110875 A066773 * A075376 A032935 A004831` `Adjacent sequences: A138758 A138759 A138760 * A138762 A138763 A138764`
	KEYWORD	`nonn`
	AUTHOR	`Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 01 2008`

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Last modified February 15 18:22 EST 2012. Contains 205835 sequences.