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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A354241 Expansion of e.g.f. 1/sqrt(1 + 4 * log(1-x)). 7
 1, 2, 14, 160, 2544, 51888, 1292208, 38012448, 1289847456, 49593778368, 2130914229312, 101188640375040, 5262325852773120, 297450338175682560, 18157597034693207040, 1190483599149657584640, 83433723762978141189120, 6224485980052510972692480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. FORMULA E.g.f.: Sum_{k>=0} binomial(2*k,k) * (-log(1-x))^k. a(n) = Sum_{k=0..n} (2*k)! * |Stirling1(n,k)|/k!. a(n) ~ n^n / (sqrt(2) * (exp(1/4)-1)^(n + 1/2) * exp(3*n/4)). - Vaclav Kotesovec, Jun 04 2022 a(0) = 1; a(n) = Sum_{k=1..n} (4 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 09 2023 PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+4*log(1-x)))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(-log(1-x))^k))) (PARI) a(n) = sum(k=0, n, (2*k)!*abs(stirling(n, k, 1))/k!); CROSSREFS Cf. A354240, A354242, A354244. Sequence in context: A354242 A268011 A052112 * A364398 A074635 A201465 Adjacent sequences: A354238 A354239 A354240 * A354242 A354243 A354244 KEYWORD nonn AUTHOR Seiichi Manyama, May 20 2022 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 September 26 21:54 EDT 2023. Contains 365668 sequences. (Running on oeis4.)