The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A277404 E.g.f. A(x) satisfies: A( x - (exp(x) - 1)^2 ) = x + (exp(x) - 1)^2. 0
 1, 4, 36, 508, 10020, 253804, 7853076, 287078908, 12106864260, 578586544204, 30901130685876, 1823983173981148, 117911755067635620, 8284976875099852204, 628692318063511556436, 51240154266491883376828, 4464155216699369664399300, 414013560595951627772296204, 40722939746084736801890208756 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..19. FORMULA a(n) = 2*A143138(n) for n>1. E.g.f. A(x) satisfies: (1) A(x) = x + 2 * (exp( (A(x) + x)/2 ) - 1)^2. (2) A(x) = -x + 2 * Series_Reversion( x - (exp(x)-1)^2 ). (3) A(x) = x + 2 * Sum_{n>=1} d^(n-1)/dx^(n-1) (exp(x)-1)^(2*n) / n!. (4) A( log(1+x) - x^2 ) = log(1+x) + x^2. EXAMPLE E.g.f.: A(x) = x + 4*x^2/2! + 36*x^3/3! + 508*x^4/4! + 10020*x^5/5! + 253804*x^6/6! + 7853076*x^7/7! + 287078908*x^8/8! + 12106864260*x^9/9! + 578586544204*x^10/10! +... such that A( x - (exp(x) - 1)^2 ) = x + (exp(x) - 1)^2. PROG (PARI) {a(n) = n!*polcoeff( -x + 2*serreverse( x - (exp(x +x*O(x^n)) - 1)^2 ), n)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A143138. Sequence in context: A138435 A366337 A008546 * A024253 A052746 A145084 Adjacent sequences: A277401 A277402 A277403 * A277405 A277406 A277407 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 15 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 1 19:16 EST 2024. Contains 370443 sequences. (Running on oeis4.)