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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A371370 E.g.f. satisfies A(x) = -log(1 - x/(1 - A(x))^2). 4
 0, 1, 5, 62, 1246, 34734, 1239708, 53958456, 2771832656, 164151829440, 11010949643640, 825134834757936, 68321156113803360, 6194283782068848816, 610322188305019432032, 64936303681095948453120, 7419917758371561069774336, 906217650382400588573066880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..17. Index entries for reversions of series FORMULA E.g.f.: Series_Reversion( (1 - x)^2 * (1 - exp(-x)) ). a(n) = Sum_{k=1..n} (2*n+k-2)!/(2*n-1)! * |Stirling1(n,k)|. a(n) ~ LambertW(2*exp(3))^n * n^(n-1) / (sqrt(2*(1 + LambertW(2*exp(3)))) * (LambertW(2*exp(3)) - 2)^(3*n-1) * exp(n)). - Vaclav Kotesovec, Sep 10 2024 MATHEMATICA Table[Sum[(2*n+k-2)!/(2*n-1)! * Abs[StirlingS1[n, k]], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 10 2024 *) PROG (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*(1-exp(-x)))))) (PARI) a(n) = sum(k=1, n, (2*n+k-2)!/(2*n-1)!*abs(stirling(n, k, 1))); CROSSREFS Cf. A368033, A371371. Cf. A052842. Sequence in context: A302181 A357350 A360345 * A307783 A319624 A182118 Adjacent sequences: A371367 A371368 A371369 * A371371 A371372 A371373 KEYWORD nonn,changed AUTHOR Seiichi Manyama, Mar 20 2024 STATUS approved

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

Last modified September 19 14:36 EDT 2024. Contains 376012 sequences. (Running on oeis4.)