The On-Line Encyclopedia of Integer Sequences® (OEIS®)

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A277413

E.g.f.: Series_Reversion( x + Sum_{n>=2} (-1)^(n-1) * x^(2*n-1)/(n*(n-1)) ) = Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!.
(history; published version)

#7 by Paul D. Hanna at Thu Nov 17 00:53:58 EST 2016

STATUS

editing

approved

#6 by Paul D. Hanna at Thu Nov 17 00:53:56 EST 2016

EXAMPLE

E.g.f.: A(x) = x + 3*x^3/3! + 70*x^5/5! + 4620*x^7/7! + 599256*x^9/9! + 128648520*x^11/11! + 41281606080*x^13/13! + 18507916627200*x^15/15! +...

STATUS

approved

editing

#5 by Paul D. Hanna at Thu Nov 17 00:53:32 EST 2016

STATUS

editing

approved

#4 by Paul D. Hanna at Thu Nov 17 00:53:29 EST 2016

NAME

E.g.f.: Series_Reversion( x + Sum_{n>=2} (-1)^(mn-1) * x^(2*mn-1)/(mn*(mn-1)) ) = Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!.

STATUS

approved

editing

#3 by Paul D. Hanna at Thu Nov 17 00:52:48 EST 2016

STATUS

editing

approved

#2 by Paul D. Hanna at Thu Nov 17 00:52:45 EST 2016

	NAME	`allocated for Paul D. Hanna` `E.g.f.: Series_Reversion( x + Sum_{n>=2} (-1)^(m-1) * x^(2m-1)/(m(m-1)) ) = Sum_{n>=1} a(n)x^(2n-1)/(2*n-1)!.`
	DATA	`1, 3, 70, 4620, 599256, 128648520, 41281606080, 18507916627200, 11049593741746560, 8474451191616009600, 8119493428719228192000, 9504049395027168805824000, 13345312208487981260926464000, 22140681034117932250214874624000, 42846437958647788197412779939840000, 95657301566159892238019686222356480000, 244038306493164073323605513327887380480000`
	OFFSET	`1,2`
	EXAMPLE	`A(x) = x + 3x^3/3! + 70x^5/5! + 4620x^7/7! + 599256x^9/9! + 128648520x^11/11! + 41281606080x^13/13! + 18507916627200x^15/15! +...` `such that` `Series_Reversion(A(x)) = x - x^3/(12) + x^5/(23) - x^7/(34) + x^9/(45) - x^11/(56) + x^13/(67) +...+ (-1)^(n-1)x^(2n-1)/(n(n-1)) +...`
	PROG	`(PARI) {a(n) = (2n-1)! polcoeff( serreverse(x - sum(m=2, n, (-1)^m * x^(2m-1) / (m(m-1)) ) +O(x^(2n+2))), 2n-1)}` `for(n=1, 25, print1(a(n), ", "))`
	KEYWORD	`allocated` `nonn`
	AUTHOR	`Paul D. Hanna, Nov 17 2016`
	STATUS	`approved` `editing`

#1 by Paul D. Hanna at Thu Oct 13 23:27:18 EDT 2016

Last modified August 29 15:31 EDT 2024. Contains 375517 sequences. (Running on oeis4.)